**See below for updated versions of this mod**
I recently added a lithum battery to my GT and there doesn't seem to be much detailed info around for this mod, so I thought I would share what I did in case anyone else wants to try it. This was based on some posts by Superkon/ Turbokon, but there wasn't much detail given on those threads.
I used the Adafruit Powerboost 1000C board which is a combined balance charger and 5.2v boost converter. Superkon mentioned in one of his posts that he used a voltage divider to adjust the voltage to 5v, but there is no need to do this as the board has a voltage divider which you can modify. The datasheet for the TPS61090 )https://cdn-shop.adafruit.com/datasheets/tps61090.pdf ) even gives you the correct value to use - 1.8Mohm (instead of the original 1.9Mohm). So switch out resistor R3 for a 1.8Mohm 0805 SMD package:
Then wire the board like this:
There may be more efficient wiring possibilities, but this method definitely works.
I also broke out the LEDs from the board to indicate battery status. For this I used an SMD RGB LED (ROHM MSL0104RGBU1
https://uk.farnell.com/rohm/msl0104rgbu1/led-red-grn-blu-700-1200-400-mcd/dp/2688619) connected with magnet wire. I put this in the TV Tuner latch hole behind some smoked perspex, and glued in the micro usb on top of it. Blue = charging, green = charged, red= = low battery. I didn't bother with the 'power on' led as it's a bit unnecessary.
The battery is a single cell Lipo (this board is only compatible with single cell Lipo/Li-on batteries) 3.7V 5000mAh size: 105080. When you remove the battery contacts in the compartment it fits very nicely without any cutting required and with space either side to remove the case screws when needed.
This GT has the 3.5" screen mod and I get around 8 hours of battery life and it takes about that or slightly less to fully charge. It can also charge while playing. I imagine with the original screen it will be an hour or two less than that. With the GT running an Everdrive and charging the battery it draws around 1.4A, so any decent USB 2A charger that can power a modern phone/ tablet will work fine, or it could even run off a power bank.
That's pretty much all there is to it, hopefully this is useful to someone.