The leakage you see looks like normal never pulled battery drip into the case leakage and corrosion. Almost every plus I've seen has a little in the battery area if not more like that.
Yeah, you are right! Another thing I noticed (before the capacitor blew up in the first Plus) was that the brightness knob made the screen flicker and pulse, I had to have the dial set just right for it to stay still... So not only that capacitor needs to be replaced, but I need to check everything else on the analog board too. ugh.

fun fun fun