I decided to go the route of a redesign on a couple of components. It was obvious that the voltage drop in the original voltage regulator was causing the regulator to be a steady 3.3V, especially as the single cell battery dropped below 3.7V. This caused the the ESP to reset occasionally. 

I've chosen an Analog Devices buck-boost regulator to replace the AP2112. Yes it costs $1.57 more than something else, but this one has a lot of documentation, and is more likely to work the first time.

After @Ted Yapo commented on my last log, I also realized that the fan motor driver I chose has a high voltage saturation need on the two outputs, limiting the power actually available to the motor itself. I've used fan drivers for other projects and like the simplicity of the part, but I redesigned the board to include an actual brushed motor driver.

I made a square, somewhat spread-out PCB to test the new features, it's an intermediate step before putting all these new parts on the board and having no space to probe. 

I sent it off last night to @oshpark's super swift service. It includes:

• Tag Connect layout! >> this one I'm really excited about
• New buck-boost >> already realized I forgot to put the thermal vias in
• New motor driver >> only one, so the the buck-boost won't be getting that hot anyway :)
• On-off linear switch (replaces annoying momentary)