I have no control over whether or not the user runs their battery flat
Yes you do. Use the right hardware.
There are plenty of combined charge/protection modules available on aliexpress that use the TP4056 charge controller and DW01B protection IC that monitors the voltage of the 18650 and disconnects it from the load once it goes below 3v.
If you are not capable of doing a proper job on the hardware end then you would be best off paying someone that can. Your approach is backwards. Fix the real problem.