Well, if agreeing to his request is going to cause you such financial hardship that you could lose your home, then the answer is obvious. SAY NO! He is legally obligated to pay, and you are entitled to receive, a set amount for the next 12 months, so there really isn't anything he can do about it. Now, if you want to be a nice guy you could consider compromising, and letting him pay less than he is obligated it to, but more than he is requesting. For me this would depend on how dependable he had been with his payments in the past, and how forthcoming he was with money for "extra's" throughout the years. Perhaps he could extend his payments beyond the original agreement so that ultimately you end up getting the right amount of money, but just over a few extra months.
Now, to me, the biggest issue is that reducing this amount by half for the last 9 months of his obligation causes you to fear that you could lose your home. What the heck are you going to do 12 months from now when you don't have ANY child support? You better start figuring out how you are going to make it then!