Thanks again for the advice!

I've never done this kind of thing before, but this seems like the kind of project one could start with, yes? Do you know of a good website or anything that might walk one through the process of removing/replacing the battery, adapting a miata battery and all that?

Also, I have to admit I'm a bit confused by your comment about using the ground when checking the battery with a multimeter. The multimeter I have, which I've used for testing computer power supplies and such, but never anything like this, just has two prongs: one goes on the positive terminal and one on the negative. Is there a separate cable that's supposed to be used for the ground when dealing with more power or am I misunderstanding you? Electronics is not my strong suit, I'm afraid.