So I decided just to try to repair the trace that was cut instead of using wire. I had to scrape away some more of the mask to expose more copper before repairing it with solder, and it seems to have done the trick. The battery is now working as expected. I think you were right about there being some sort of transistor that shorts TX to GND because it was shorted to GND before powering on the drone, but wasn't after.
I'll keep an eye on it to make sure it works as it should. Thank you for helping me with this!