We agreed on Friday that he would practice at least 12 days out of the 16 days he has off school for break. If he did that, I'd continue lessons. He hasn't touched the piano since.
I saw this earlier but didn't have time to comment. I think that if you made this deal, you need to stick with it. If you really feel that he will ask to go back after a month off, then maybe you could pay the teacher to hold his space.
This reminds me of when my niece was given an ultimatum by her mom that if she didn't get a project done by a certain date that she would no longer be allowed to homeschool. When I heard about this, I looked at my niece knowingly and acknowledged that she had no intention to finish the project. She got a huge grin on her face and said of course not. She didn't know how to tell her mom that she wanted to go to a traditional school. Her mom was very invested in homeschooling and was convinced that regular school was the ultimate punishment. Maybe your son is saying that he wants out of piano? If so, why force him to continue at this point? It sounds like time and energy that could be better spent elsewhere. After 6 years, he's not a frustrated kid who can't handle the challenge. I like the idea of getting him into another instrument.
For my kids, I think that the greatest value has come from the adult/mentor relationship. With my DD who is 2e, we have had various phases where she just needs a break for a month. Her teacher has been willing to work with us. We haven't paid her for the time but we've always managed to work back into her schedule though not always at our preferred time. Dd likes piano but she really misses her teacher who also acts as an informal therapist. I've decided that I value that relationship too. Now, I don't stress out as much when she doesn't practice enough.
