I know you said that you read 61.31 over and over, but 61.31.g.2 says you have to receive and LOG training from an authorized instructor IN a pressurized aircraft (or sim). That is all in addition to the ground training specified in 61.31.g.1. There is no OR (unless you logged PIC prior to 1991 in such a plane).

You better check with your local FSDO.