Well it seems the problem is that your rig is on its side

No, just kidding. And I'm glad you started this thread because I've been mulling it over but since I couldn't come up with any tidy, for-sure, easy fix, I hadn't said anything. By starting the thread, well... so here are my thoughts.
Actually, before I start, just to let you know where my thoughts are coming from: Boats are built somewhat similarly to the Chinook shell. Especially the roof, which is a cored construction -- fiberglass boat decks are often cored. The reason for a cored structure in the first place is that it is very strong and rigid for its weight, without needing deck beams (i.e. overhead frames akin to roof rafters/joists). The way it achieves this rigidity is sort of like how a steel I-beam works. (Caveat here is that I am not an engineer of any type - this is just what I know from some experience, reading, and a little bit of osmosis from real engineer types.) The way the I-beam works is that it takes two flat pieces that would normally not be strong enough for the job, and makes them the top and bottom plates on an I-beam. Then a vertical piece is introduced and fastened securely to the two top and bottom plates. By holding the top and bottom plates firmly, and keeping them a distance apart from each other, they are much much stronger for their size. The bigger the distance they are held apart from each other (i.e. the taller the I-beam), the stronger.
A cored deck works similarly by holding things in tension. The top and bottom "plates" are the relatively thin top and bottom fiberglass skins. The vertical piece that holds those skins securely -- and apart -- is the coring material. In the case of my Chinook roof it looks like "Nidacore," which is a plastic core that looks a little bit like a honeycomb. in a perfect world, everything is sized appropriately, and then built impeccably so that the top and bottom skins are well bonded to the core (if, for example none of the parts were bonded together, you'd just have three floppy parts - two floppy fiberglass skins and one bendy core - it's the bonding that makes it work).
So there are a few things that could compromise this:
1) The parts just were never up to the task (core not thick enough for weight that will be on it, etc.)
2) The skins weren't well bonded.
3) Water has gotten in somehow and the skins have become de-bonded.
4) The fiberglass layers themselves weren't well bonded together (with resin) and have delaminated.
Okay, so the above is what I think we have going on in the Chinook. That is, a cored roof construction. Even if #'s 2, 3, and 4 have not occurred, we could be seeing a bit of #1. That'd be my first guess. Basically, the Air-conditioner is a heavy point load (110# or so), right in the middle of the "deck" and .... right at a weak point (i.e. a 14" square hole in said deck). Now take that and bounce it down the road for a couple of decades, plus just let gravity act on it. I can see how that could cause a sag. It doesn't take much of a sag to make a little "lake," around the Air-con unit, and the gasket was never designed to be "under water" -- plus it's not sealing to a flat surface any more. I think it's unlikely to ever cause a problem with the entire roof, but as you have noted, a depression right where the air-conditioner unit is, means water can pool right around that gasket.
(Oh, BTW, we have determined [in another thread] that yes, the Air-con condensate simply runs out the side (or maybe sides) and then runs off the roof (by design). So that could easily account for the water on non-rainy day. And if it's muggy out (hello Ohio!) then there will be more condensate, I think.)
So, on to possible ideas. I do hope others will post as well. I think member Scott may have dealt with the same issue to some extent (?) and would have some experience with it. I could see juuuust the whisper of a sag beginning on my roof when I removed the Air-con, so I'd think this is not unique to just your Chinook.
*****
So, there are definitely ways to do a "proper" repair and make it better than new and so you wouldn't see any evidence of it when the job was done. You'd repair a boat deck this way if someone brought it in to your shop for a full, professional repair. But those ways would be pretty disruptive to both the interior and the roof. And your Chinook is not going to sink in the middle of the ocean like a boat might. My guess is few people would want to do a repair of that extent to a Chinook roof. So how about other ways that aren't just how you'd do a fancy boat job, but also aren't complete hacks? Hmmmm.....
Well the challenge is to basically make a repair to the middle/edges of a hole, but the hole still needs to be used by the Air-conditioner.
I first thought about filling in the depression (well, the edges since there is no middle) around the top, where the air-conditioner sits. Using something like thickened epoxy, perhaps with some reinforcement. After all, it's mainly the outside that needs to be flat. All the mess would be outside, and while you wouldn't want to leave it hideous, it's not like it would need to look as perfect as a part of the coach you can see on a daily basis. If there is room, perhaps some reinforcing angle around the edge of the opening too. This would need to stay relatively stable after the repair so the epoxy/glass wouldn't want to crack. What I don't know is how sagged the roof is, and how "hard" it is to un-sag it - plus how much does it want to re-sag. This would also involved relatively few materials ($). You would need to remove the air conditioner (but you could keep it on the roof just away from the hole). I removed mine in about two hours, including lowering it to the ground, so it's doable. I was solo or it would probably have gone faster.
If you were removing the Air-con permanently (which I realize is not a practical option in Ohio!), because the Air-con would not be squatting over the 14" x 14" opening like a big fat mushroom. So I could envision some "easy" options with making a skylight with a structural frame that also reinforces the roof (picture a smaller version of those buildings that have the structural beams above the roof). But I still think that concept might be good.... somehow.
So, the concept of some structural "beams" that go somewhere, and you jack up the roof just a tad and then place the beams. Once those are in and the roof is no longer able to change, then if there was a depression left over it could be filled (would hopefully be smaller and less dynamic then). If I remember correctly, member Scott who has a 1994 (?) had a similar issue and did (or is doing) something along those lines (albeit removed the Air-con). Maybe he will pipe in.
But in the meantime, so... how to actually enact the concept. Beams on the roof are not desirable because they could be water dams. Also the air-conditioner overlaps the area adjacent to the 14" square opening. Although something that mimicked the metal railings....maybe? Far enough apart to miss the Air-con overhang? Boats often have handrails similar to that. You'd have to consider how to "catch" the roof structure with them.
Or maybe tackle it from inside: Some nice wooden cross members that are like the deck beams inside a boat could help and look nifty too. They are often made by laminating a bunch of thin pieces of wood together so they curve correctly. Wouldn't have to extend down into the rig much more than the Air-con shroud? Or use painted steel for thinness? There might be less need to "Sandwich" the structure with fasteners when going from below because gravity would be on your side, pressing on the beams (you'd still have to hold them up, but perhaps not quite as involvedly).
Another idea that is less "radical" and might still help: You can buy pre-made "FRP" (fiberglass) sheets from McMaster Carr. These are sort of the plywood of the fiberglass world, and come in various thicknesses. Say you'd buy a 24" x 24" of, maybe..... 1/2" thick GRP and cut the 14" hole out of the middle, then bond it to the roof around the hole. Now, bonding one of those to the roof is not going to remove the sag, but oftentimes on boats things that go through the deck sit on little "islands" in the form of base pads. This way, although they see their fair share of water, they are never just "sitting in" pools of water. I'm pretty sure the Air-con can go through a much thicker roof, because "normal" stick built RV's have roofs that are thicker, more like house roofs (studs, insulation). So what about getting a sheet of "X" thickness high quality fiberglass board, and bonding it to the roof on the outside (maybe with a wee bit of thickened epoxy filler to help the sag a bit). Now this sheet would essentially become part of the roof. I don't think that would be enough strength to single handedly hold the sag out, so I'm not suggesting you jack things way up before applying necessarily; but what it would do is raise the Air-conditioner - and its gasket - up out of the lake, plus add a touch of stability (minimal laminated layer effect). We're talking "just work tidily and follow the instructions on the can" type of epoxy work here, not high art. I'd say like building a sawhorse vs. a dresser. You'd be doing the sawhorse
I found myself wondering about the idea of not just putting FRP on the outside, but also putting a matching sheet on the inside, all bonded, so that the roof sandwich is now thicker (via the skins not the core, but that still puts the outer skins further apart). Painted light grey or white, it would not look bad I don't think (air-con shroud is there anyway). I think it might help.
These are all just musings, so I'm not saying to just start on any of them. I'm just thinking out loud about it. It's always more of a "okay, how should we tackle this one," when it's a repair on an existing structure, vs. starting from scratch. I hope others will chip in as well and we can continue to bat ideas around and then hopefully come up with a plan.
BG