Thanks for the reply.
I did disassemble the speaker and none of the caps appear to be puffed or leaking, but I assume they can still possibly be bad.
However, I took a (cheap analog) multimeter to the tweeter in the bad speaker and there was basically no resistance across the leads of the tweeter. They are cloth-dome tweeters, so I don't think that is normal, it might be blown.
I'm kind of scared to open up the working speaker and pull the tweeter from it to test with because it is working beautifully..! I went ahead and ordered a replacement tweeter which should arrive soon. Will update if it works.