If you start singing, patting, swaddling while he is nearly asleep from feeding, you are actually disrupting your LO from falling asleep. Imagine yourself being disturbed by phone call while you're almost asleep. You will have to calm yourself down again and take a while for you to fall asleep. With your LO, he is tired already, almost asleep, and then WOW all those stimulations! He is now overtired, and needs longer time to soothe and to fall asleep.
Try to gently remove him from feeding, hold him for a while and shs, put in a dummy for your LO to suck and lay him down in the bed. Keep everything subtle and calm. My LO doesn't like patting, too stimulating for her, so I just put my hand on her tummy to assure her I'm there and do Shs...
Just wondering, is your routine EASY? or is your routine AESY? Or, EAESY?