There's two possible approaches here, and it depends which one you feel more comfortable about tackling: an electrical (low voltage DC) wiring challenge, or a case modification challenge.
Firstly, you could look up the pinout for the 7200 PS connector, and re-wire an ATX power extender cable. MacJunky's link should turn up a guide, if not for the 7200 specifically then for a model that uses the same PS. I recommend using the extender rather than re-wiring the lead from the PS because it allows you to swap the ATX PS for any other in the future should you need to.
If you'd rather approach it as a case mod, you can use the existing, working 7200, and mod whatever is necessary in the ATX case to get it to fit.
There are a few reasons why (IMO) the second approach might be better. First of all, obviously you already have a known working PS, so there's less to purchase. Secondly, you're already booked in for a certain amount of casemodding re: the 7200 backplane.
Third, in terms of doing a beige ATX conversion, there's not going to be any re-wiring involved: the beige logic board is designed to use an ATX power supply (and in fact does in the Tower G3). There's a jumper on the board to select between an ATX PS and an Apple one. So if you feel you need practice at anything, I (personally) would get busy with the casemodding.
Best of luck.