On raising your price to make them leave: I would not, and it is worth saying why beyond the ethics.
It often fails. They say yes, and now you are doing work you did not want at a rate you named, which makes it much harder to leave later - you set the price, so the problem is apparently solved.
It is dishonest in a way people can feel. You are hoping for a no while pretending to offer a yes.
It teaches you nothing. The actual problem here is not the money, it is the weekend messages and the reversed decisions. A higher rate does not fix either.
Where a price increase is legitimate is when the money genuinely would change your answer: you would happily keep doing this at a rate that reflects the disruption. If that is true, say so plainly: this level of availability is a different service and here is what it costs. That is an honest offer and they can take it or not.
But you said you want out. So go out, cleanly. Using price as an indirect way of saying something you could just say is how people end up in a second year of a job they resigned from in their head twelve months ago.