How serious is your under bite? i had underbite issue, i was told the same as your orthodontist told you. Braces > Surgery > Braces (3 process) was quote around 60k+- all in.
But i did not go for the surgery, only braces but they did remove 2 of my teeth and my wisdom tooth and slowly adjusted (take 5 years to complete my braces) no more underbites issue after my braces..