SOLUTION for the benefit of google searchers: I can't solder due to the aforementioned "hot-snot," but I did manage to pull off a minor act of finger contortion and hold a 100uF (25v) cap on the TP4056 output whilst plugging in the servo to my board. That's the answer: Add a decent sized cap between your TP4056 and the 5v boost converter.
Thanks, jremington, my train of thought would have not gone down that track without your assistance.