I have a TFV4 as well on my Lavabox, but I use the RBA section. 12 wraps of 28gauge ni200 @ 500F. Preheat is 100watts and the wattage is set to 40watts.
I like the idea of putting a bigger battery in the lavabox, but I myself would not want to extend the device in any way. Just ruins the look of the device IMO.
A Flight Power PWP2133 would almost fit 67 x 33 x 20. Just over by one mm. http://www.flightpowerbatteries.com/fp25.html What about buying individual cells then wiring them up in series ?