Dunno if anyone has already mentioned this about the 1200 PSU, but it was designed to run EITHER a 2.5" Hard disk OR a Fast mem card / CPU accelerator.
(It is actually rated at something like 23 Watts.)
I ran a Desktop 1200 for a good while with a 2.5" HDD and an Apollo 1230Lite Accelerator with an IDEfix'97 4 way buffered IDE card on the original Supply. however, it sometimes needed time to warm up, was a little flakey with Hardware stretching screenmodes (modified Super72 Monitor) and the CD I had on the IDE board was on its own supply (External case).
I have since towered it up, and have added an External Keyboard adapter (A4000 keyboard, naturlich !) a Silversurfer (clockport serial adaptor) for me modem, and a CD/Amiga audio mixer.
if you do what you stated above and get the AT/ATX PSU sorted you'll be well away.
PS- the higher clock rates usually demand more power, but you knew that anyway !