I don't believe you cannot get +5 from a console joystick. Unless its because some consoles don't power their sticks with +5 (as far as I knew all of them did)....just hack the cable going into the controller.
Anyway, you should be very carefull if you plan to power the P360 with an external power source. From looking at the diagram on happ website, there is a +5, GND, and 4 directional pins. This mean that the power supply ground is shared with the directional swtich grounds. This is not good if you plan to use an external power supply (other than the console's ground and +5). You do NOT want to tie the external power supply's ground to the console pads ground...you could possibly fry the joystick port.
I'd ask around some more to see if anyone else has done it this way (as far as I've herd they either get it from the console pad, or if its a mame only machine, they get it from the PC power supply).