You are way too kind - this feels embarassingly like getting too much praise for this, and you'll probaby call me a cheater in a minute (and I would understand!).
So here is what I did: First I machined the kit's ring down quite a bit on the lathe (it is still in there, under the blue part). Then I used Fusion 360 to create the design, which is not all that complex (circles at the ends, hexagons 10 mm in each side a little larger than the circle, a bigger one in the middle, then a loft between all that and some manual twisting followed by splitting the resulting body into three parts).
Now here comes the cheating bit: I have a tiny desktop CNC mill that I used to produce the three parts. I used what Fusion calls rotary toolpaths, and the line variety of this, which means the part will rotate in very small increments (1 degree on the final pass) and the milling tool will go up/down the length of the part, following the contour of the part. So to all those who admired my pen for the workmanship: your praise goes to a soulless machine. My apologies! I'd love to be able to produce something like this just using my hands and a not quite so clever machine, but I also love the possibilities the technology offers. If this is frowned upon here, please let me know and I will not show any CNC produced pens again.
There was still some minor manual work involved: the CNC mill cannot machine all sides of a part, so cutting off and cleaning the side where it is attached to the stock is of course a manual process, as is some sanding and polishing etc.
The problem with the gap is the turned off centerband from the kit. I should have turned it down to the diameter of the tubes (I left it a little larger), which would have given me a little tolerance to use in assembly.
@Spanx: yes, this would indeed have been another possible way to achieve the same - except my mill only has a working area of about 3 inch in each axis, which is not large enough to produce a full one-barrel pen in one go.
Side note - I showed this to a relative who is a professional machinist, and asked him if this could be produced on a lathe. He believes it is possible, but would need a special lathe mostly used in the manufacturing of car engines.
Side note 2 - theoretically, I think there might be a way to do this without CNC. You would need a mechanism that links left/right movement to the turning of the part (similar as what happens when you machine gears on a lathe, only with a very different ratio), and work with a sander of some sort while turning the part by hand, i.e. sanding the contour rather than turning it in the traditional sense. Not sure if I am making myself clear...
Really amazing work.
