But I use a little different path to turning out my own fillers- not better, just different, and it uses 2 dedicated tools......
The first is a self-centering vise, sold by Penn State Industries, that clamps to my drill press. It allows me to easily drill on center, no matter the size of the wood blank. Let me show you....
This is the vise clamped and ready to drill-
To set up, first you close the vise on your drill bit-
Then clamp the vise, open the jaws , insert your blank, close and it's centered, every time. I buy my blanks on the internet and they come in all sizes, and this vise keeps that thru-hole right down the middle, slick and easy. And because the travel on my 8" drillpress is so short, I can drill, flip the blank over, and center drill to complete from the other side-
Drilling the blank as the first step allows me to mount it onto a mandrel (another tool from Penn State, used by pen makers) for turning on my lathe-
After bringing the blank into round using a chisel, I use a cutting tool in a holder, like Joe, until I am just barely oversize, and sand paper to my final width-
Next, the reel seat filler goes into one of Bob Vennerri's mortising jigs. I have clamped a straight edge onto my router table as a fence, and Bob's jig holds the filler securely as it passes by the fingernail bit-
Another view of the mortised filler held in the jig-
this spalted maple filler is ready to sand and finish, and then it will wait until the next set of split strips finally takes shape as a quad or hex, and the filler becomes the part of a rod upon which hangs a reel, and hope....
Doug

It reminds me of my old
self-centering doweling jig for woodworking that I still have but never use anymore. A grand idea if you need it.