I removed the screws along that right side of the panel, and the top and bottom corners. The outer layer of caulking pulled away quite easily and was pretty stretchy, but wouldn't really hold the "stretch" before breaking. Based on BT's previous description of products, that acted like silicone to me. I found a few cracks and other holes in the outer seal, so it seems like water may have gotten in their over time and maybe swollen the underneath supports. Otherwisey I can't really tell what's going on behind the panel (I don't know what to look for quite honestly), but the lower screws that are pulled outward (the images in my first post) wouldn't snug up... the underlying surface holes were too chewed and opened up already. For now I'm going to get some longer screws that will tighten better, and look for a latex product to seal it.
Anyone ever done a complete repair on this type of problem? Or HAD it done someplace? I'm not opposed to having a pro check it out eventually, if it won't cost me an arm and a leg.