That's good advice, and I have seen that thread before! Unfortunately I don't think a standard ATX PSU will fit in the IIx, because it has a longer but quite a bit narrower power supply than the IIci/IIcx. Hence my decision to go with the TFX power supply. I am going to be using soft power... in fact, it is already installed and working in the photo I posted earlier. So really my primary remaining challenge is how to physically fit the TFX PSU into the old case in a way that works properly. I think I have a handle on how to do it; it is mostly a matter of finding the time to get it done.
I'm going to try to take pictures as I go along so I can post either here or somewhere else publicly accessible to document for posterity.