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Our first step is to determine if the compressor keeps running or the heating elements are what keeps running.If the elements are what keeps going, the issue id most likely a sticking sequencer.
If you have a volt meter we can troubleshoot to find out exactly what is going on.
Looking at the diagram that jumper is supposed to stay in place to make sure reversing valve is energized anytime W1 gets power.
Now if the reversing valve is staying in heat mode when you go to cool, we would want to troubleshoot the reversing valve and see if we are making and breaking voltage at the solenoid.
Either way, even if reversing valve stayed in heat mode, when thermostat is satisfied Y should lose 24v and cut compressor off so that would not cause the issue you are having about it still blowing hot air.
We can go from here.