The problem is not that he thinks f his crate as punishment, it is that he has control over elimination now and he likes going in the house. The correction lies in not giving him access to the whole house and establishing a significant sacrifice for errors. There should be an immediate reprimand to identify the error coupled with time out in an unfamiliar place like a small room, or a period of shunning where he is totally ignored.
play pen use
Since he does well overnight I would suggest that you don't change that routine. We have found adding a pen after the first couple weeks does make for a nice transition between just the palace and free run of the house, I would suggest using that to expand his environment during the day when you are not actively engaged with him, once he demonstrates that he returns to his pad from the pen then you can expand his area even further. If you are going to have him away from the palace and pen you can also take the pad and tray with you.