the manufactures website says max 264vac input, 277 is just under 5% more. When these are engineered/designed they have a safety factor built-in and it should run fine on 277V.
http://aplus-powersupply.com/products/bitcoin_powersupply/bitcoin-miner-power-supply-ap188/
Here are pictures of the power supply.
http://imgur.com/a/LUURV
Ideally, I would just like to remove the over voltage protection, not the ground fault shutoff.
Anyone have any ideas to try?
No one responsible will recommend you do that, if you start a fire then it weigh on their conscious if you were hurt. Just get a proper circuit installed.