Getting the cowl panel off is not that difficult, but getting it back on correctly can be a real pain. One bolt at each end, and a hidden one in the middle hold it down, then tilt it up at the front and gently work it loose (after removing the wiper arms, of course) There are clips that hold it in place under the bottom of the windshield, and getting those seated properly when reinstalling can be tricky, and it is necessary to do so otherwise the panel won't fit right at the back. The curved molding at the back of the cowl panel is held on by plastic clips that also hold the metal tabs that engage the clips under the windshield. The whole thing is badly designed, relying on brittle plastic and far more awkward than it needs to be. This was corrected for the 90 model, when the complicated mess with all the clips was replaced by a plain simple rubber molding. Undamaged early type windshield bottom moldings are EXTREMELY RARE (I've only seen a couple in over a hundred cars I've looked at) so if yours is intact, be careful with it.

As for the clog, if it is clogged, a lot of debris must have gone down past the loose screen, as the openings the water runs off through are quite large. The inner panel is mostly solid, with an oval hole on the passenger side for the heater/vent air intake. This hole is surrounded by a plastic rim that is designed to keep debris and water out of the heater even if it makes it past the primary screen. Water is supposed to run off to both sides, and down through the inner fenders and rocker panels and out. If the drains are completely blocked the wiper motor will probably be partially submerged---if that's the case, I'm surprised you haven't had problems with it.

If there is a lot of debris under the cowl, the rocker panels are probably full too, and should be cleaned out. This is not as difficult as it sounds. You have to remove the door sill trim (front and rear, both sides) pull back the carpet and pry out some round (2" diameter) plastic plugs you will find in the inner rockers, then use a shop vac and a coat hanger wire to remove all the leaves etc.