We took out a loan from my fiancé's credit union. We are both getting sleeved in Mexico so we took out enough to cover surgery, airfare, extra hotel room for my mom who is going with us, & passports. We will use our savings to cover any bills if needed while I'm out on FLMA. My fiancé is using vacation time so he'll get full pay while off.
Good luck & I hope you're able to secure a method to get the surgery paid. We felt the extra $400/month payment was worth it for our health. I'm guessing you might feel similar because having kids is riding on it for you.