I meant to try to fix my mic, and I finally did it! Actually, it turned out to not be broken.
To find that out, I first had to find it, which took 40 minutes because I stuffed it in a bag labeled "headphones". Then, I spent some time searching for my preamp before I concluded that I probably threw it away.
When I plugged it into my mixer (which I probably got because my preamp wasn't working), it registered signal right away. After some wrangling with Pulse Audio Volume Control, I was able to test recording through it on my computer.
Without even turning up the amp from quiet practice volume or doing any special mic positioning, it already sounds better than the amp modelers I've used and certainly better that the iPhone mic (which is actually rather good for a phone mic).