Sounds like he is getting OT which is impacting his nap and then his night. The nights sound like OT NWs to me.
I would suggest doing your usual WD for nap, get him to sleep the way you usually would, leave the room, then just before 30 mins go back in quietly and see him through the transition with a W2S (begin your usual soothing method either before he wakes or the second he stirs). If he fully wakes do what you usually do to sooth and also tell him something like "it's sleepy time, you need to sleep, go to sleep". At 1yo he is likely to understand much of what you say and if not the words then the general tone. Continue using W2S or soothing until he is asleep. Leave if you can when he is asleep but return for the next possible 30 min WU and repeat.
Whilst it may be hard work I really think it is worth it.
Before dropping to 1 nap mine did a very routine 2hr nap, self settled, had always done this, it was a guaranteed nap, set your clock by it yk? But when he dropped to one nap it totally messed up. OT waking every 20 mins. I spent several days with him in my arms screaming blue murder mid nap and he'd cry on and on until eventually falling to sleep in arms and I'd lay him down telling him "I'm putting you in bed so you can sleep properly, call if you need me" then I'd leave again. The disturbances were way too much, too long, too much screaming etc although I knew it was worth doing it to get him more sleep.
When I started doing W2S for the 20 min WU it was so much easier for me. I 'perfected it' by crawling into his room at 19 mins putting a hand on him and rocking slightly as he woke and transitioned (still OT) and I could leave the room at 21 mins. I had to go back in 19 mins later for the next one...and I did this for a full 2hr nap.
Because i was helping him to avoid OT he gradually caught up on his sleep and got back into the swing of the 2hr nap. So if you are lucky you may only need to be in there a few mins, fingers crossed eh?