Put him to sleep in a bouncy seat. One that reclines. Put that seat in the baby bed or on the floor beside you so that he is in your sight. Since he's so young I'd make sure his little head doesn't bobble over too much. Maybe roll up washrags and put one on each side of his head to keep his neck straight?
Our little guy had reflux so much. It was awful.
Things you can do. Feed every time you get a chance, never let him get too hungry. The crying for food gets air in his tummy and gets it all churned up. So those times will be more likely to have reflux.
Our doc gave us liquid Reglan. We have him .9 in a tiny open ended syringe. He'd gobble it down, it smelled like oranges. Reglan relaxes the tummy and helps it open up on the bottom quicker. So the food goes down quicker into the area where it's digested and used. It helped a LOT.
Then we decided to always put him in the bouncy seat to sleep. He never laid flat. If we didn't have the bouncy seat we used his car seat but again, we took precautions with his neck so he wouldn't flop over and suffocate.
When he got to be around the age where he wanted to turn over he started getting fussy in his sleep. So we let him lay flat one time on his back. He promptly rolled over and went to sleep. He slept like that from then on. He was able to turn over and do what he wanted.
But you are right about overfeeding. That's the main cause for reflux. Avoiding overfeeding is the best way to combat reflux.
IF the reflux IS due to too much stomach acid being produced then an acid med is needed.