According to SM, it’s a 3/4 x 12 thread. So, making one with a scrap of aluminum bar would not be a huge issue. A tap that size is too large to be included in a typical kit, I’d expect somewhere in the $20 range. You’d also need a few drill bits that are bigger than a typical home DIYer would have, so making your first one could cost $40 or so, just on the tools. (And it would be better to use a drill press for this, but you could use a hand drill, going up in size from 1/4 inch, to 3/8, etc.
i‘m pretty sure I made a mount using one of the “router bases” that come with dremels. Some creating cutting and epoxy were probably involved. (Didn’t realize it was a standard thread…)
My shop went through several dremels a year. Their quality has gotten pretty bad—Michael, if your old dremel is still working, just buy it some new brushes, and be happy with it. The two issues we had with ours (at my shop) were the speed switch getting dirty (easy fix) and the bearings going (not easy). I switched over to buying Proxxon rotary tools—much much nicer and almost trouble free. (Carried by the large online bookstore.)
On the other hand, if you only use it for the odd fret polishing, or rare drum sanding, a Dremel would probably be a 10 year plus purchase.