I am in the process of fixing the same issue...I have some pics but have not had time to write up a post yet. You have identified the issue, there needs to be a drip edge along that outside seam to keep the water from creeping into the floor. Mine was built just like yours, OSB with a hard surface applied to it.
I have the floor out of my slide now and am replacing with 2 pieces of 1/2" plywood laminated together with Titebond III waterproof wood glue. I applied 4 coats of Spar Varnish to the bottom and edges. The bottom needs to be a somewhat smooth and slick surface because as the slide comes in, it rides on 5 nylon blocks installed at the edge of the main floor.
The problem with the OSB is that once it swells you are done. If you want to try and fix it, first thing is it needs to DRY. Tarp the slide out and use a hair dryer. Get some of the rot doctor and the injection kit and shoot it in the OSB floor. Once it dries/hardens, then you can trim the floor back to the original thickness and I would coat the bottom with several coats of spar varnish.
For the drip edge I got some plastic J-channel for drywall, and cut it down:
Tarp setup:
My issue:
Here's the edge:
The factory coated the edge of teh OSB with what looks like Plasti-Dip or Flex-Seal, and it cracked over time...as the water got in due to lack of a drip edge, it swelled the OSB, opening the cracks more, allowing it to absorb more water, which swelled it more, etc etc.
