Instead of the recess (so you can have access to the two batteries inside the GP2x cover), you might be able to incorporate a larger battery compartment to fit a pair of C-cell batteries (at a push). You can get rechargable batteries for C-cells at about 9,000NiMH, as I recall, which should give far longer game play between recharges. Just a suggestion, if you have some spare space remaining, as per the pic. This would also take out the risk of cutting your fingers or hand during gameplay with the sharp edges (as per pic).
Do you have enough space for this?