I agree, your best bet will be the removable ATX tray type with back panel I/O ports built in or attached to it. That way all you have to do is cut a hole for the tray's back panel and find a way to mount the tray, which shouldn't be that hard assuming you can get it lined up well. There's really not much option for drilling and tapping your own ATX layout holes with all the big gaps and the old aluminum/steel sheet spacer holes.
The old case I have that is similar to that has HUGE power supply in it (3 times as large as the usual ATX formfactor). IF yours is similar, a good bet is to make an adapter of sorts out of good sturdy sheetmetal. Cut holes in it to match the wider case holes (Or wherever you can find the space to make your own mounting holes for bolts/rivets if the supply isn't as large), then put in your ATX sized holes for exhaust, switches, plugs, and mounting in the middle (Either one large or several small individual holes, as you see fit). Also a good idea to make L-brackets to help support the power supply while you're at it.