You wouldn't use up-ducts, they go in the ceiling (that you don't have). (-sorry, didn't mean to confuse-)
I think a window a/c should be fine. Cool air sinks & warm air rises- you'll have to try it, I'm not sure if it will vent out the soffit vents well enough- you still might
need an exhaust fan for best circulation. Make sure the bottom of your garage door has a good rubber seal on it, otherwise you'll lose a lot of cool air under it, &
lots of wild creatures may also want to come in.(for cool air or the rodent perfume, lol) Also, make sure the door into the house has good weather-sealing
on it (to help keep out the garage air).