J.,
All 5 of my babies had reflux, and against doctors advice, I slept all 5 on their tummies. My personal experience is that I have seen them sputter and choke during the day when laying on their backs playing. I want to sleep when I can and know I won't if they could choke on their spit. Plus, they all had strong necks and move and lift their heads from the start. They occasionally had a damp cheek, but to me it was better than suffocating on spit.
I did (still do for the babies) keep the bed at an angle as well. And, there are no bumpers or extra blankets for them to choke on sleeping. This is a tough one, and it's your call. But, my sister in law told me the other day they found that a gene causes sids.