To my knowledge no one has found a successful therapy for rehabilitating a weak LES valve. I think for some people if they reduce their acid level for several months, then some of the damage will heal, and if they make lifestyle changes to reduce the demands on the LES valve, then they can almost feel normal again. This has not been the case for me.
I have tried a variation of hyperbaric oxygen therapy to try to improve my LES valve, which is to greatly increase my aerobic fitness. If you elevate you heartrate on something like an exercise bike several times a week, you are greatly increasing the oxygen levels in your body tissues through elevated blood flow. This will give your body the best chance of healing and mending itself. But so far for me this has not caused any noticeable improvement in my LES valve strength (although being in better shape makes GERD easier to deal with).
I've been trying to think of other ways to exercise the muscle tissue of the esophagus to see if that might strengthen it. Some people that have trouble swallowing are able to strengthen the swallowing muscles by doing exercises where you lay on your back and raise your head and hold it up repeatedly using only your neck muscles.
Exercising the LES valve muscle is more challenging since it is not a voluntary muscle. The only way I can think of to exercise it directly is to lay on a bed that has the head elevated, and put my feet at the high end of the bed, and then swallow food so that my esophagus would have to work hard to push it uphill. But if I do that then acid will probably leak out and damage my esophagus during the exercise. So maybe that idea is even more out there than hyperbaric oxygen chambers, but as you say the doctors don't seem to try anything but medication or surgery.
I keep wondering why no one is doing stem cell injections into the LES valve to see if the valve can be regenerated at a cellular level, but I've not heard of anyone trying that.