DD was a tummy sleeper from birth, even in hosp she would NOT settle unless she was on her tummy. Both boys managed to sleep on their backs/ sides - I found if they were unsettled being on their side was better. When they were older I used a rolled up blanket against their tummy & that seemed to soothe them better than being on their back withtheir belly exposed.
But I stressed out & worried the whole time too. I have an angelcare monitor this time... from all the PPs seems that's the way to go.
It does seem if babies decide they want to be on their tummy there's not much you can do to change their mind....good luck with it all