My journey of discovery ended quickly.
I called Hilstead Heating & Air, they don't mess with window AC and refered me to appliance repair, Central Service on Monona Ave.
My notion of a "freon injection' is ancient, that procedure has been illegal for many years. Besides, freon leaks are not so common, and a 10-year-old AC probably wouldn't work at all by now if it had a slow leak.
No, the problem is probably that the mofo is dirty and dusty. It needs an enema. Central Service will clean an A/C if you bring it in for $40. Or they send two people out to remove and clean it. $75 for starters.
Uhhh, I think I will do my best to clean it myself.