I had the same issue in the same locations. I know it will be hard to get the unit dry up there, compared to here in NM, but that is the most important first step.
My leak was the slide seams on the ends leaking and on the roof seam from front to rear. I used an epoxy penetrating wood restorer on one end of the slide to restore the wood to a hard durable condition. I cut out the rot on the other end since it extended about 1 ft into the wood. The epoxy restorer worked fine but I think the total removal was a better fix. Just not as aesthetically pleasing. Anyway, I was left with a 1/4 inch raised floor on the front end of the slide due to the overlap to secure the patch. You have to keep the bottom at the same level, obviously, so be careful not to have any screws, etc. extend past the prior level bottom.
I used Henry's EPDM paint, primer, and fabric tape to fix all the seams. That stopped the water intrusion. I Wrapped the EPDM fabric and paint around the bottom of the slide and made a small drip ridge on the bottom edge. All I did was pinch the fabric tape up and paint it with the EPDM. I sealed every seam horizontal and vertical even if I did not think it was the current cause of the leak. A gallon of paint and primer goes a long ways so you might as well redo the whole slide roof while you are at it. Do not forget the seam where the rubber gasket attaches to the slide.
Hope this helps and it may sound tedious but it is just one step at a time.
