Yes its possible to relocate the power jack, there was even a mod done by a guy that basically put a female mini usb connector in place of the power jack, which takes up half the space and would allow you to charge off of any usb port at the full 5 volts.
The charge mod from my understanding limits the voltage on the phat to 2.5volts which increases charging time.
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With the relocation of the power plug up near the sony logo, if you use the original female power connector you might run into limitations with space, unless you have the battery cavaty available, such as the battery extension mods I've seen.
Other wise you might think about getting the psp slims (or similar) female power connector as it doesn't have the weird 2 prong thing like the phat does...I believe those were originally meant for a weird sound dock but was never utilized.
With the second nub, the ground wire is providing the current that will be supplied to the buttons. Most people have a misconception that on a battery the power flows from the positive to the negative, were in reality it is the opossite. (If I remember right)
So thinking that way you will need the ground inorder to send the right information to the buttons to allow "movement".