Ok, unfortunatly you are out of luck on this. I really hate when there is an industry wide standard and OEMs decide to make their own stuff to prevent any sort of upgradeability. This is worse then dell integrating the power button, usb and audio into a proprietary circuit baord and cable to to the motherboard.
There is no option for you to upgrade your power supply, HP only made a 400w model which is not enough power for a 7870, probably would not even power a 7770/r7 260. Not only is there no plug and play option, you could not even go so far as to hack and resolder wires as the cables/voltages do not even match the ATX standard.
Thus you have one of three options:
1) Sell the whole damn computer and build one that is not a...