Down.. and out
I am sorry that you are no longer enjoying teaching. Work-life balance may have been the mantra of the last few years, but it isn't easy to juggle the two. Write a simple letter to your head stating that you are resigning with effect from August 31. Keep discontent or recriminations for a verbal discussion, then it won't be on file. You have until May 31 to resign, so why resign now when you don't have another post to go to. Start looking, and even applying, for another post. You can either resign when you have found one or reconsider if you don't find anything suitable. You are not in the position to be without a job, so don't put yourself at a disadvantage.
Consider the reaction of anyone reading a reference from you current head that started "X has resigned without a teaching post to move to...".
Regarding supply, unless you are a talented teacher in a shortage subject, this may not be as easy as you think. Check the supply teaching threads on "The TES" staffroom website. Is there anyone in the school you can talk to about improving your lot in case you can't find another job?