One principle I learned from the first book I ever read on turning (old
bodger name of Frank Pain) was that you can't get a catch if your cut is
above the wood. *Inside, that means below the center, outside, above.

Seems to me you got this exactly backwards. Inside below center the
catch drives the tool into the wood. Same with outside above. Inside
above center a catch drives the tool into air. Same with outside
below.