I'm the one who posted about my Dd sleeping longer on her tummy :] here's how the transition started:
At about 5 weeks her daytime naps were only 20 minutes long and she was overtired all.the.time. I tried swaddling, incline sleeping, side sleeping, you name it. Nothing worked. After talking to my mom I decided to try having her sleep on her belly for one nap, on my bed. I stayed next to her the whole time. She slept for over an hour! So I gradually started putting her on her belly for all daytime naps. I would stay next to her at first, then I started watching her on the video monitor and checking on her periodically, etc. After having her sleeping at night next to me in the RnP since the day we brought her home, we finally decided to put her on her belly overnight last week and haven't looked back. She consistently naps 1 to 2 hours at a time, and will sleep from 11pm6ish, eat, then sleep again til 9 or 10am. The first few nights I constantly woke up to see how she was doing, now I only wake up and check the video monitor [i can see her back moving as she breathes]
I'm ok with putting her on her belly for the following reasons: she's had great head control since birth, it helped with her gassiness in the early weeks, she has no other risk factors for SIDS [low birth weight, exposure to second or third hand smoke, etc]. And yes, belly sleeping increases the risk of SIDS but the odds are still very low. We weighed the pros and cons and ultimately made the decision we think is best for us.