You can reinstall the trim strip and the vinyl bulge for esthetics, just don't seal behind it or underneath it (or on top). It just traps water and guides it into the holes. Proof of this is the shaft of the screws being rusted, so you know water is going in there. The stripped screws are common, they overdrive a lot of them there and elsewhere, they are only going into the bottom shell most places.
The bomb proof fix is to fiberglass over the joint which carefully done could look fine. Remove the gel coat to a tight line just above and just below the bump (structurally you need more below the bump but aethetically you'd want it to be even), tab carefully inside that line, paint the stripe to match or a contrasting color. It already has a bump and trim all the way around. It would be more work but a little cleaner to cut off the upper shell overlap before tabbing, the tabbing could be narrower and the bump would be less thick.
If rescrewing instead, I'd go up to the next size screw so that the pilot hole cleaned the hole of dirt and old sealant, carefully - with a torque limiting driver - drive in the new screws, then remove them, coat them in 5200 or whatever, and drive them back. Other than the very front where wind might drive water up under it, the seam is unlikely to leak as gravity is very dependable. It is the screw holes that leak. I've thought about removing the screws, wedging the top away from the bottom slightly and cleaning out the seam then resealing it with 5200 prior to putting the screws back but it would be probably as much work as just glassing over it. Would maintain the factory look though.
It's too bad the factory doesn't tab the shells together on the inside prior to installing the interior. It's probably half a days work for one guy at that point and would make the product far better.