How did you previously deal with NWs? Was he always nursed to sleep? I would suspect if that's the case that even if he was an independent sleeper at BT that he had an overnight prop at night wakings. Now he's not nursing it could well be that he has transferred that prop to being picked up and cuddled before he is willing to settle again.
What I would suggest is instead of going in and picking him up that you go and sit next to his bed. Gently tell him to find his lovey, lie down and go to sleep. Don't do it for him, he can presumably easily get from standing to lying and is able to move around to find his lovey? Try to avoid physical contact if you can as it sounds like that might be what the issue is. (Obviously though use your judgement - if he occasionally needs a cuddle just to calm him if he has become hysterical then trust your instincts on that. It should be the exception rather than the rule though). There's likely to be shouting and screaming to start with, but you are not abandoning him, just being a comforting presence while he works out how to settle himself on his own. If he is an independent sleeper at BT it really shouldn't take him long to understand what you are asking of him. After a day or two, move so that you are halfway to the door. And then another day or so later, into the doorway, then outside. If you are consistent and do the same thing for every waking, he should learn quickly
Routine-wise my only thoughts would be how long has he been on one nap? He's still pretty young for it but if he consistently naps 3h it's probably do-able. Most LOs with a 3h nap would need at least a 12h day though - it may be he needs the short day at the moment because his nights are so broken but I would have expected if he starts getting better quality sleep that you will need to extend his day otherwise you will end up with BT resistance or undertired NWs.
Hope that helps to start with