Following advice from Graeme and Grant, I bought and tried out an ordinary ATX PSU to solve my PSU problem but unfortunately it hasn't worked out. It fits in reasonably well, with three of the screws able to go in, and only a small gap, but it's not got what I need.
The IBM system has two additional "AUX" power connectors, with eight and ten pins each. But standard ATX PSUs only have a single AUX connector, with only four pins.
Fortunately Adelong Computers have a 7 day return policy, so I can take the PSU back in on Monday. I'll take the IBM PSU in with me and see what they can suggest.