I think i will start from checking the refrigerant pressure first, easiest and cheapest to rectify the issues before i move on to the larger problem.Have to check whether the clutch not engaging or your air con refrigerant is low. When refrigerant is low it does not cool fast either especially in slow traffic. Once you speed up the compressor turning fast so the refrigerant works faster and at the same time at faster speed the condenser gets cool faster also.....
Thanks,
Ken