I think the larger RPis will fit "in a fashion" since RetroPassion IS selling prebuilt kits with the RPi3A+ so it's possible. However, the CM4 is a minature RPi4 spec board without the IO so will fit better. Claude has designed a neat IO port and cabling solution routing to the back of the A1200 case and Michal has designed an adapter board that both allows the IO cable to connect and provides an internal SD slot (for the EMU68 software) as well as providing a low profile way of attaching the CM4 to the 'lite' PiStorm32 model (we ideally would have got a 'full' version of the PiStorm32 board without the need for an adapter but the parts are unobtainable at the moment).
I view the CM4 solution as the ideal and think it'll fit in the A1200 better than the current RPi3A+ solution sold by RetroPassion and it will give more MIPS. If you have a spare full RPi in your sock drawer then I guess you just give it a go and see how well it fits otherwise go the CM4 route! Obviously, we're still at early doors and some testing still needs to be done with the incoming adapter prototype boards but I have faith that Michal/Claude will overcome any obstacles as they seem to know their stuff. Make sure you buy a lite version of the CM4 board to get SD card functionality on the adapter board and any more than a 2GB model is a waste (I went for a 1GB model). WiFi functionality is being worked on for the future (so get a WiFi model if that interests you) but all CM4s support ethernet, USB and HDMI.