The TXV acts independent of the compressor cycling and reacts on incoming ambient air temperature. High ambient will mean more refrigerent flow, less ambient less flow. If the TXV is sticking, then to produce warm air it would have to not allow enough refrigerate flow to meet ambient air temp demand. The compressor cycling is determined by the two temperature sensors on the evaporator, one on the inlet air and one on the outlet air to keep the evaporator from freezing up. If the TXV is not allowing enough flow then the evaporator will not be cold enough and the temperature sensors on the evaporator will not tell the compressor clutch to disengage. Since it seems there is enough refrigerant then I would look at the compressor clutch when you are getting warm air. If it is engaged then it's probably the TXV, if it's not engaged then it could be one of the temperture sensors, or even the A/C control unit.