For the mamas that nurse to sleep

My LO is 12 weeks old, i still nurse him to sleep. The only issue I have is after he falls asleep on me I have to wait 20ish minutes to put him in his crib. If I put him in sooner he thrashes around and keeps me up anyways (also he's started rolling back to tummy so he will roll onto his tummy if he isn't fully out and I have to roll him back onto his back since he just starts grunt/crying).

Just wondering how to reduce this time so I can have him nurse to sleep and then just put him in his crib (he wakes 2-3 times overnight and I'm dying for more sleep). I'm wondering if I need to sleep train him and completely remove the association with feeding and sleeping or should just gradually reduce the time he gets to sleep on me each night?