Pictures of someone's work often makes a guy critique it. What comes to mind is a lot of questions such as what did he do before, why did he do it like that, how much work was that compared to the alternative and why is this a better way. In this case, since he can't put the whole barrelled action through his headstock, he needs to hold the muzzle without damaging the crown. I would have used a plastic expanding insert inside the bore to hold that end in the tailstock [a little bit of runout is not an issue with a belt polisher] but he decided to build that contraption. But, I'm sure he does more than just polishing with that assembly. This device, akin to a steady rest jig, has been discussed before and I know I have considered it. Easiest solution is to buy another steady rest and use your action jig. The reason I haven't bought another steady rest is simply money VS requirement. I should check out my cost of another steady.
Its good to see different ideas, that is certain.