I personally would take the OB up on the offer of Reglan provided they are willing to prescribe an effective dosage for this purpose. There are some dangerous side effects of Reglan and you have to limit the amount of time you take it AND taper down the amount you take gradually.
This is why most people would prefer to take Domperidone instead of Reglan however it is much harder to get Domperidone in the US and insurance won't cover it. (I'm actually taking Domperidone because my Dr wouldn't give me an effective dosage of the Reglan so it didn't work.)
I wouldn't wait till after the tongue tie correction to get the Reglan, now is when you need the extra help with your supply, hopefully once the correction is done and physical therapy is done and baby is nursing better you will be able to taper down and get off the Reglan.
I'm not sure what to tell you about the supply worries, I'm still struggling myself. I've been on the Domperidone two weeks and dropped the supplements 5 days ago so I'm white knuckle about my LO's weight gain (but he isn't giving me cues that he is still hungry after nursing so I'm worried about his appetite.)
Hang in there momma, you are not alone.
Call the ENT office and ask them to call you if a cancellation happens and you can get in sooner, and keep calling them to see if you can get in sooner.