Wanting braces again to close the open bite but I don't want to relapse/get surgery. Am I eligible for Fastbraces?​ (photos)

As I see it, your main problem is the open bite. That is likely caused by your tongue. Even if you had braces and/or surgery to close the open bite, if your tongue is still pushing/posturing forward, the open bite WILL come back. I would suggest talking with an orthodontic specialist and try to get a referral to a myofunctional therapist. Most likely, you will need to be taught to do some exercises that will train your tongue to not go forward when you talk or swallow. The bottom line is that the cause of the problem (the tongue) has to be addressed in order to have a long term fix of the bite.