Data recovery from 2016 SSD with dead battery

33 days after the warranty expired on my 2016 MacBook Pro (15"), my perfectly healthy battery stopped charging. Unfortunately, I failed to notice until my battery was at 2%, and too late to back up my data to an external drive. I should know better by now.

The folks at the genius bar believe the problem is a energy management failure on the logic board, but informed me that fixing the problem means replacing the logic board, and losing my data (I'm halfway through my master's thesis, and feel sick at the thought of loosing my research and writing).

I learned there is a proprietary tool that will make data recovery possible, but that Apple will only recover your data when they make the repair under warranty. Geniuses did not present this as one of my options and instead referred me to VERY EXPENSIVE third-party data recovery specialists who will remove each of the 16 chips to extract data.

There is absolutely nothing wrong with the drive, other than the fact that I cannot get power to it. Anybody have any ideas on workarounds?