I know you're looking for ideas regarding the best rainy-day disney park, but, if you don't mind, I'd like to be a bit more specific by adding my favorite rainy-day attraction: Illuminations.
A couple of years ago, we were about to leave Epcot as Illuminations was beginning (with a pretty substantial rain). Before we left, though, we decided to get a peek of the show. It was incredible; the show, IMO, looked completely different from the non-rainy Illuminations. Because of all the water droplets in the air, we could see every laser beam and light effect that usually goes unnoticed. Sure, you can see some of the lighting effects because of the smoke; however, the rain makes it perfect!!!!!!!!! Trust me, Illuminations is a must in the rain. We actually hope that it will rain on nights that we are at Epcot. Oh, and don't worry about getting wet. Your day is almost over anyway. :wave: