Well, speaking from experience, my dh and I went throught the same exact thing when our ds was only 5 weeks old and we finally decided to give in and let him sleep on his belly rather than endure all night/nap screaming. Our ds too, would cry and cry and then the instant we placed him on his belly he would fall asleep and be happy and content.
However, if its possible, I slept even less than I did when he was so upset on his back. I was paranoid about SIDS (sudden infant death syndrome)!!!!!!! I kept the monitor on the highest volume just to be able to hear him breathing and often went in to check on him at least once an hour. I just kept asking myself, "Is this really worth not hearing him cry?"
But....just like many things with motherhood, we "freak out" in the beginning of a new situation, after awhile, we calm down a bit and by the time a few months has gone by, we feel silly for ever having worried in hte first place. So, our ds is now 6 months old and a wonderfully happy baby that continues to sleep on his belly at all times.
It is a major decision, though. I personally, was too afraid to speak with my doctor about my dh and I's decision to let ds sleep on his belly beause I thought for sure I would get lectured or worse, have the child protective services (CPS) called on me.
Through all of this, I found out that my SIL and 2 friends experienced the same problem with back sleeping and all of their children are fine, healthy, and happy. Also...you have to remember that when we were babies, our parents were always told the opposite, "Never put your baby on their back because they could choke on their own saliva/spit." We all turned out fine (or so I like to think
)
I hope this helps. Good luck! Let me know if there is anything else I can help with.
-Christine