Quick update - I added a 1A fuse between the battery and the USB charging and protection board, and that is how I plan to leave it. I took these measurements after installing the fuse to see what voltages the charging protection board would cut off the battery:
Battery Low Cutoff 3.04v (with 1A fuse in series with battery)
Battery After Charge 4.22v (with 1A fuse in series with battery)
These work for me, but I am still not really happy with the performance. I tried a 5V regulator board and a 5V fan but the performance was only modestly improved, if that. I think I need to go bigger on the fan to have adequate solder fume extraction, but this will work in a pinch.
Lithium Battery TP4056 DW01A Charger Board Module
3.5A DC-DC Step-up Boost Voltage Converter Module 3V 3.3V 3.7V to 5V 6V 9V 12V
(could not find the exact link but there are tons of these tiny boost controllers on Ebay)
I used the 12V version, the voltage should match the fan being used.
FBApluto 15pcs Female Micro USB to DIP 5-Pin Pinboard 2.54mm Micro USB Type Interface Power Adapter Board 5V Breakout Module (I used these for the fan and battery connections)
3A/250V 6A/250V switch:
(Pack of 40 Pieces) MCIGICM AC 3A/250V 6A/250V 10A/125V 2 Solder Lug SPST On/Off Mini Boat Rocker 2pin Toggle Switch Car Auto Boat Round spst Rocker Switch
Gikfun 12x12x7.3 mm Tact Tactile Push Button Momentary SMD PCB Switch with Cap for Arduino (Pack of 25pcs) AE1027
nidici 20pcs(10 Pairs) 1S Lipo Charger 3.7v Battery Charging Cable Male & Female for RC Quadcopter Drone Multirotors
Carbon filters (used these), the filters linked below are for garbage can deodorizers.