Well you can still birth at home. Independent midwives usually don't care what your BMI is - mine has never asked how much I weigh, and nor would she.

As for payment, well some come with payment plans so you could probably pay with the baby bonus after the birth if you asked them?

I'd go with the home birth option, then fighting the hospital where you feel most at peace in. After all, it is your body that has to go through it, so you are the one that has to be comfortable. And if that means you have to lose a little bit of weight, then maybe its worth doing?