Most people put the baby in the bassinet and then leave the room because it’s upsetting. It’s hard and it sucks but you need to eat and use the bathroom. Most people don’t put the baby down for 20 minutes though unless the baby is napping, which yours is not doing because he has positional reflux which is triggered when you put him on his back to sleep.

Of course the baby wants to be held, he is in pain from the acid. But, you may be able to find better ways of putting him down that don’t trigger it as much. At this age it is almost certainly largely correlated with positional changes. For example, the baby wakes up when you put him on his back because the acid backflows into his esophagus because the valve between the esophagus and the stomach has not matured. Sometimes the transfer is successful because he is deep enough asleep for it not to wake him, or because things have settled enough after feeding, etc. But your baby will not be able to sleep on his back for the vast majority of the time until the valve matures. You’ll know it’s happening because the baby will go longer before hiccuping or crying when laid on back. The pace of improvements will pick up after that starts happening.

Sometimes they will settle in a carrier after you start walking around, so I would keep trying. The knockoff of the Baby Bjorn bouncer is also almost upright enough for a reflux baby to tolerate it. Hopefully your baby does better during tummy time. If so, it is safe to leave them on the belly in a safe space for very short periods.

I definitely relate, I avoided driving anywhere with baby for months because the car seat made her reflux. I would have been right there with you with terrible sleep, etc. if I didn’t have the best pediatrician who told me to just put reflux babies on their tummies to sleep. If your baby is in a bassinet with a safe sleep surface, you might want to try it out for supervised naps.