They do NOT need a signed lease to put the utilities in their name.
I would make very certain they understand:
they will not move in until after the utilities are in their name.
they will not move in until after all the deposit and rent is paid in full....in cash.
If they are like this now at the beginning of the tenancy..do you know they are going to be even worse once they are in??
Slow pay is the path to no pay.
Never sign a lease until after all money is paid...never. You cannot prevent them from moving in now. You will have to give them propery 1 full month notice or you will have to evict to get out of it. Never sign a lease without full payment. I learned that the hard way...looks like your are going to learn it that way too.
Can the agreement they signed prevent them from moving in? It says they agree to pay a certain amount on April 25, put the utilities into their name before May 01, and pay the remaining balance in full by May 11 and if they dont do any of this then the deposit they put down to hold the house on April 25 will be forfeited and all agreements voided.They dont have a key to the place as the agreement says it will be given to them on May 11 if the terms are met. I only agreed to hold the house like this because they assured me that if I would they would do the agreement. With this happening before move in I suspect they will have problems later on. I put that the deposit would be "forfeited" to cover if they couldn't do the terms and help reduce my costs on passing up potential tenants if they didn't work out.
You are being worked over by an experienced deadbeat. Offer to return all their money and move on. Make sure you get a letter signed that they give up all rights to the lease. If this does not suit them, hold on to the key and do not let these people move in. It would be sure to cost you a lot of money later.