It has been a revelation to me that the medical science does not yet have a clear etiology on the root cause behind the transient relaxations of the LES.
In some cases, it is distension of the stomach after a meal that can cause it. In other cases, nervous system disorders or imbalances can cause it. Stress, anxiety definitely has a role to play - but I am not convinced it is the root cause. GERD is very tricky. GERD can cause anxiety which can then cause the GERD to get worse. So, the cause and effect can get all intertwined.
Vagus nerve controls various functions and tLESr is one of them. So in the absence of other causes (hernia, being overweight etc.), it is a good idea to target it. Antidepressants, benzos etc. do help in that regard. In my case, I can not tolerate these drugs either. So, I've been using other natural ways (yoga, meditation, therapy etc.) to calm the nerves in some way.
So, you should definitely give these drugs a try and see where you land. I do know a person in my town who got better once his job became less stressful.