It's so frustrating when we do stuff like that (and we all do it). I never do my binding that way. I prefer the traditional folded binding because I think it will hold up better than a single layer. Especially with the frequency of washing these will get. I just use something from my stash. The backing they select for the kits doesn't usually look right for binding anyway.
If it's not too much work, you could piece the batting back on and then recut it to the size you need. You might have a lot of ripping to do though.