When I barrel M1 Carbines I use a Brownells action wrench with the head for a M1 Carbine receiver and a barrel vise with a profile made to fit the barrel forward of the chamber. the Carbine receiver is somewhat fragile and can be damaged w/o the proper tools. Brownells also sells a barrel paste which I use on the barrel threads for installation.
I clamp all of my barrel vises for the Carbine, M1 Garand or M1903 in a 20 ton shop press- no movee there. The Brownells action wrench has replaceable heads which are specifically made for a variety of receivers incl the Carbine, Garand, M1903, Lee-Enfield, Mauser, etc. You just swap heads onto the wrench depending on the rifle you are working on. It's a good investment for someone who wants to get into gun plumbing in a serious way.