Having seen your jigs, you probably have a better solution. 

This is how I've been doing it.

The only reliable technique for tube I've found and use, though it takes patience and a steady hand, is to roll/score the tube under a sharp, heavier, hobby blade. Preferably not on a cushiony base, as that will encourage the tube/rod to bend under pressure.

After enough turns, it'll just snap off.

Pushing too hard will indent the tube.

I sometimes use an awl to flare the tube back open.

For tiny rods, I just cut, either with PE snips, or larger ones, small pliers. Of course, I cut just a tad longer, and file/sand the end square afterwards.

I do have a mini tube cutter, similar to a plumbing pipe cutter, but the issue with that is the support points don't accommodate really small lengths, like in this project.

I should probably try heating the brass before cutting, maybe that would speed up the scoring(?).