There used to be a jig setup used a long time ago to make files that I think would work very well for draw filing barrel flats. I'm going by memory here so please forgive...
The idea is that you want to file something very flat (originally, the piece of metal from which you wanted to make a new file). You held the working file in hand and did the usual draw filing. But, the part being filed was allowed to freely pivot on axis.
With a barrel, one could make a cone that stuck in the muzzle and had a bearing so that the cone could freely rotate. The back of the barrel would require something a little different unless the breach plug was removed. But now the barrel can spin fairly freely. So when filing on the top, if the file is tilted even slightly, the barrel just rotates to stay flat against the file. At least, as long as there is at least a little pressure between the file and the barrel.
This should allow a person to go faster as one doesn't have to be careful to stay flat on the barrel, while doing an even better job. And when you want to change flats, just rotate the barrel instead of unclamping it. Actually there seems to be a lot of unclamping and reclamping when draw filing, at least how I've done it so far.
After my mill is finished being relocated and my heavy gunstocking bench is finished, and perhaps a couple rifles completed, a jig like I've described goes on my to-do list. Sounds like not this decade
Gerald
PS - My recollection is the technique predates longrifles by at least a thousand years, and if I'm recalling correctly more like two, so probably some gunmaker somewhere did it. Unless it was a guild secret of the file makers or some such group.