Adobe, You must have amp'd the A/C unit to come up with the "about 17 amps". Then you say the name plate states 22amp min circuit ampacity. You have to use the name plate rating. So 22amps @ 125% is 27.5amps. You have to run #10. I got this from reading 440-2, " Branch-circuit selection Current" using the last sentence. The 22amps on the name plate does not take into account your 125%.
And to add fuel to the fire: Why is this not considered a continuous load? Some motels I've stayed at the A/C stayed on all the time.
Tom