Back sleeping

My baby is 6 weeks old. He has reflux and has a terrible time sleeping at night because it hurts him so bad. I’ve tried keeping him upright for 30 minutes after eating, putting him at an incline, nothing helps so I end up putting him on my chest and he sleeps great. I know they aren’t supposed to sleep on their stomachs but he can lift his neck easily and pushes up with his hands. I also have an owlet monitor that I use. Opinions on letting him sleep in his stomach?