You need to mount your engraver solid and then have a vee block to hold the muzzle. You can make the vice to work, but it won't hold the muzzle also. You're not planning on using the motor are you?
Make a couple vee block vise jaws with a taper or make a collet and bed the barrel in the collet with JB Weld. It takes very little clamping force to hold a barrel.
The motorized units work well on a flat surface or a small part of the barrel if the OD is large. The carbide cutters are not made to cut beyond about 1/8" off center of a 1" diameter object.
I may have a few misc. pieces that may help you.