I'm still not sure what I did wrong, whether I reversed the leads, or whether the Visar just doesn't take 7.5V, or what. I'd also kind of figured that there'd be some protection, so in the event of overvoltage (or wrong polarity), nothing bad would happen.
That's not the case, though. As soon as I hooked the leads up, I heard a loud snap, and the radio began emitting an acrid burning smell. I kind of figured the radio was toast, but I didn't confirm that until this morning, when I opened the radio up:

It's not all that obvious in the picture, but if you look at the big metal part on top (I've never worked with Visars, so pardon my lack of knowing what naything is), where it says "4597A," and then look down, there's a little black chip that's literally blown apart.
It's also not too clear, but the metal casing to the right of it is all discolored, as if by heat.
Moral of the story? If you must use a Visar, don't make blind guesses when hooking power leads up to it.[/img]