Hello,
I remember this stage well, it's so frustrating.
Tbh, I think you just have to ride it out. The best advice I got was to use as much A time as you can to practice, practice, practice his new skills. This should hopefully make this stage go a bit faster.
It sounds like what you are doing is the right thing - going in and reassuring. The hands resting on him sounds good - if it's helping him to go back to sleep, all well and good, b/c you don't want him to get out of his sleep pattern, then set himself up for a dose of overtiredness.
One thing though, I'm not too sure what you mean about the firmly tucked in blanket, but it's possible that you should re-think this, now he is mobile. If there's any chance that he could shuffle around and get himself stuck, worst of all get his head stuck, then it's not worth the risk. Have you tried a sleep-sack, or even just some really warm pyjamas/footed onesie?