You could get the phone, then don't put the EE sim in it. Get a Three PAYG instead and use that. The cash you put on them never runs out, I've got one that's had £3 on it for about a year.
You'd need to check that the phone isn't pre-locked to EE. Usually phones only lock to the provider once the sim is inserted, but worth double checking.
I think Three sims don't lock the phone to them, but that's worth double checking in a Three store when you get the sim.