John,
On our 1991 Contessa we had the same problems plus leaking windows. We removed all the windows and resealed them. We also removed all of the trim you described, once we removed the trim we realized that the trim had not been sealed properly at the factory. We scraped all the trim to bare metal, (no small task). We should have used butyl tape to reseal the roof and side trim, instead we used Eterna Bond. Walls have leaked over the rear windows since, have thin strips of clear plastic over the seams for now. You might want to consider also removing your large awning, found out rusted and rotted screws and woods. Joys of owning an RV!!
Jason Worman