Balance staff (preliminary)

I have several broken watches in which the problem appears to be (at least) that one of the balance staff pivots is broken. I'd like to build my experience to the point where I can fix this problem, which involves making a new balance staff. Fortunately, I have a balance wheel with this issue that doesn't go with any watch that I have. So, I attempted the repair on this part first, knowing that failure wouldn't be much of an issue.

I started with a 1/4" steel rod, which I turned to fit the 3/16" collet I have for my lathe. Unfortunately, my lathe seems to take 4C collets, which aren't very common. The smallest collet I have is 3/16", so that's what I have to use.
After two tries, I was able to turn a passable start at a balance staff. That is, the balance wheel fit the rivet nicely, and the pivot came out intact.

The picture above shows the view of the new (left) and original (right) parts. I wasn't careful with the lengths, and I haven't yet cut the second pivot. At this point, I needed to reverse and regrip the staff in the lathe. If I had a suitable small collet, this would be easy. But I don't, and therefore needed to hack something.

I came up with the idea of gripping a pin vise (which happened to have a handle 3/16" in diameter) in the collet, and the part in the jaws of the pin vice. The vice seems to run true, but it took a bit of doing to keep the end of the vice straight. In the end, there was a bit of runout, which I'm not pleased about.

Again through the microscope, the new part is on the bottom.

Staking the balance wheel.

Post staking... It's securely attached!

Roller table reattached. This is a taper fit; I probably made it too loose, and was able to push it on by hand (in the staking tool).

Finally, a picture of the finished assembly, to show size.

In the end, it went together pretty well. The major remaining issue is how to regrip the part in the lathe without runout. Of course, there is the possibility of running between centers, but I don't have centers made, so this would involve obtaining such as setup...