"On the use of a .22, I am not sure he could have found FMJ ammo for his SAA or the .357, either."
No, I don't know of any FMJ ammo at that time, but....
There was easy access to the next best thing, and which nice met the spirit of the accord by not having an exposed metal tip.
.38-44 and .357 Mag. metal capped rounds from Remington and Peters that were originally brought out as a means of dealing with the heavy sheet metal in the cars of the auto bandits.
Two nice boxes...
http://picturearchive.gunauction.com/8786220416/6904016/ae70cbc3249c20b0c79aa53fbcd6780d.jpg
My Uncle served in Korea during the unpleasantness there. My Grandfather sent him a Colt or S&W .357 Magnum and several boxes of metal capped .38-44 ammunition.
Come to think of it, though, Remington MAY have been making metal capped .22 Long Rifle around this time frame, as well.
I still find it impossible to believe that Patton would carry a .22 Long Rifle in the field in a combat operations zone. Patton was a gun man, he had been around them his entire life, and he knew what constituted an effective cartridge. More than that, he was a practitioner of that, given that he had killed at least several men during the Mexican Expedition.
He would carry smaller, less powerful handguns when not in the field. Those served more as accoutrements of office than actual fighting weapons.