I am glad to hear you found that article helpful. As you likely know - I have been braiding, “not just Japanese/Kumihimo” for a rather long time -
So long ago in fact, that more than once I accepted various forms so censure for using unusual threads and OMG - EEEK Beads.
With the advent of the disk and those who embraced it for simplest braids, often with beads for jewelry and accessories -
Michael’s measurements work quite well and (forgive the pun) Mirror the traditional style
When you move to novelty threads and beads and other inclusions, a bit of different thinking may be needed.
The first evidence of that is when the BeadSmith changed their Disc design to a 35mm from 25mm. Not quite the 38mm Kagama No Ana (center opening) Michael specifies,
Which leads to a LOT of Rube Goldberg experiements and some of a more refined nature with Tim Hale of http://www.fiberartistsupply.com
As you already know, the purpose of the “dip” is to allow threads to be suspended, thus “evening” tension.
the problem is that many novelty and beaded threads they do not suspend freely with a shallow bowl.
After making Michael (and others) nuts, several agreed that yes, the traditional desire could be modified to give more air, BUT as much as possible the same degree of angle should be maintained.
Some - who did not braid with novelty threads except in their nightmares, suggested more counterweight - and that had been my first idea, but as you know that just elongates the stitches and leads to loose braids - not usually what you want.
my solution was function over form. Instead of a “graceful curve” I asked for a thicker mirror (we ended up with two layers) so that the “drop” was straight sided like a round cake pan
I found that a 1;5 inch drop from out rim to Kagami no ana, worked well me and was reasonably close to the traditional
what I Liked, was a 2 inch drop The deeper drop does not seem to affect the finished braid.
I envy you the 3d printer, it is so much cooler than cheap cake push bans with their center cut out with grommets around the cut and round wooden frames from a craft store for the outer rim.
In keeping with the push pan - you could probably make inserts with various sized kagama no ana to be used for different projects.
Another day maybe we can chat about your tama design choices. I am curious