OK I'll try to post some of the things I know.
Maximum charge seems to be 4.2V although after it reaches this value it will slowly lower to I believe about 3.9V before it starts to charge up again.
Minimum operating voltage seem to be about 3.0V for a successful shutdown.
With the camera off and just charging, the camera draws 25mA
(<- Correction 250mA not 25mA). Yes only 0.025A. I feel this is the BIG problem and most likely the reason caps won't work unless the charge circuit can be modified.
(<- Correction this does not seem to be an issue.)
The minimum capacitance that I have tested and got to work (on the bench) with a full charge was 6F.
(<- Correction 3F not 6F).
On the bench (ie no GPS) my camera draws less than 500mA while running and charging. It does have a spike or two up to about 700mA but steady state is less than 500mA.
I knew the larger capacitance will take longer to charge but I'm also hoping it will take a lot longer to discharge. What I have noticed is that the lower the voltage gets the faster it loses charge. That makes sense if the power draw is constant based on P=VI. So far with the 12F
(<- Correction 7.5F not 12F) bank I have had 4 on/off cycles with it operating as expected.
Later today I will try to run some tests to see how long the 12F
(<- Correction 7.5F not 12F) bank lasts from full charge to camera off and how long it takes to charge.
Lastly, I looked at the code to try and find the values to edit. Unfortunately, I'm a bit illiterate when it comes to this kind of coding. I think I found the 1 min & 5 min values but couldn't find the rest. That confused me so I gave up for now. Really hoping someone that's better at it could modify it for me to test.