Update: Let's face it. This trailer needs more work than I thought it did when I bought it... and I'm certainly a riveting virgin no more. How cliché is that?
So I did a lot of waterproofing and skylight-improving. I put new seals around the vents and sealer around seams/rivets. I made a scraping tool from a coarse sawzall blade held by vice grip pliers, and used it to get some soggy carpet from under the cabinetry. So the leaks are mostly stopped and the floors are mostly saved from rotting away any further.
Then I finally had a chance to dump the contents of the black/gray tanks, and it revealed yet another problem: The dump valves leak into the belly pan. I guess the vast clumps of old solids masked the problem before the big flush and clean. But now the trailer smells like a French public toilet in late summer.
So now I must r/r the toilet flap seal from the top and do the harakiri of the belly pan to get to the dump valves from the bottom. Electric sheet metal shears are on order.
I have a feeling it's going to get worse before it gets better...