It's OK if he flips over when you're doing PUPD, he may be just trying to find his own position to sleep in. Let him flip about in his crib, only pick him up if he is really crying hard and then only for a minute. Don't do PUPD for 20 mins and then nurse to sleep - if you're going to do it, you need to stick with it. If you stick with pUPD he should be going to sleep independently quite soon and then your helper won't need to walk and pat him to sleep
At this age most babies are transitioning to 2 naps per day, so I wonder if a little more A time may help him to take two slightly longer naps?