I think, in your position, I’d get some of the copper sink-pads at 20mm made for the XM-L and reduce it’s dimension to 16mm, then reflow the emitter onto it which should be fairly easy as it’s designed for this emitter.
I am planning the same thing myself and have never done it before. My plan is to mount the sink-pad on a 1/2” aluminum bar using JBWeld, then use my cordless drill to turn the pad slowly while cutting it down with a grinding disc on my dremel tool. This should keep it perfectly round (or very near so) while keeping the emitter pad centered. Then cut the JBWeld off the backside of the pad and clean it up a bit with sandpaper. Laying the sandpaper on a glass surface, or formica, it’s easy to keep the part neat and flat when sanding. I also usually use a rotating pattern when doing this sanding, to ensure I don’t lean to one side…but still check it often during the process.
It’s my plan to use a 6” SS disc I have and put it on the burner element of a glass top stove. This will keep the element working properly and give me a good hot base to bring heat up in the copper sink-pad to reflow. I’ve seen some that recommend simply killing the heat when the reflow is accomplished and leaving it to cool naturally so as not to interfere with the joint or the emitter by moving it. I plan to relocate it to the glass stove-top though, to cool somewhat faster than that.
Like your plan to put copper in the core of the pill. Never have been able to understand why they use brass instead. Cost in that small of a part is offset by machining costs as far as I’m concerned, so add the extra buck or two to the finished light and call it efficient.
Will definately watch to see how you go about this build, the copper core in the pill really interests me.