I already tried changing the relay bit it did not make a difference. I would like to try adjusting the gab but I don't think I am inclined enough to do it myself and the few shops I already asked mention they do not do that they simple change out the entire compressor.

Can anyone recommend a shop in the Hamilton Ontario area?

 

Your issue is electrical in nature as the main components are giving you good, cold air when they function. I had the same issue in my 2008 Civic EX (1.8L). It would blow cold air and then you'd notice it was merely cool and now more humid. Honda at first replaced a compressor relay they claimed had failed..didn't work. Next, they replaced the Evaporator Temp Sensor...didn't work. Last, they found a failed clutch and coil. At last, they got it right. Given your observations of the clutch, I'd first check the clutch and coil before they rebuild your a/c piece by piece. Good luck.