My eldest did this, particularly at night. I remember spending many nights pacing around the house carrying my little one to soothe her, only for her to get upset when I stopped. Mine liked to be upright, with a gentle rocking motion and being able to stretch her legs (which I suspect is the main reason for the kicking when you stop.)
There isn't a huge amount you can do about it and it's one of those movements that is hard to replicate. Babywearing will help (I loved my cloth sling, it was fantastic) and if nothing else it will at least free up the use of your arms - but it's unlikely to do anything about the walking around because your gait (walk) clearly provides the right rocking motion for him.
Give it another 8-10 weeks and things should change (things can change a huge amount from month to month or even week to week at this stage) without you having to do anything other than keep them clean, comfy, and fed - they will get to the rest on their schedule.