When I worked on three projects on the main slide....it lived under this cover for a month. Stayed dry, wasn't pretty but did what it was suppose to do.
If you want to take the corner off. Might consider 'dropping the front of the 5er down a little in the front, so gravity flows in that direction....and wrap the slide corner to cover it up if you need to. You are only protecting the one edge and if it rains, by theory everything should flow to the front.
Sounds like you have re-caulked about everything I can think of.
When you said:
One thing I didn't expect to find was strips of rubber roof material placed around the corners but not glued. Not sure I understand that. Do you have a picture? Or is it the corner at the top of the slide flanges where the top and side meet.
If you don't want to leave the trip on and remove the 'wet' screws. try building a 'tent' over the open removed screw to allow it to breath and protect the hole.