For years I have used a Dremel mototool in a Dremel drill press, but I have modified it to be more solid...it is still not solid enough, and I hand sand the ff holes to final size. I think the way to go is Proxxon, a much more solid system. Dremel tools are pretty crappy generally. I stopped at the local "big box" to look at them a few days ago, and 3 out of 4 of the demos had slop in the chuck bearings (actually in the housing as on one I could see the whole bearing move!). Several of my Dremels have slop, and a couple don't, but I wouldn't count on them staying that way. Should I ever upgrade, I would get the Proxxon.
Basically, a larger 3/4" board is fitted to the stand permanently, and a 1/8" pin is drilled into the board and centered under the bit. I made a mandolin ff hole template out of 1/4" plex, and it is double stick taped to the bottom of the top plate after it is completely carved. I use the grout removing bits (reground).
It does work really well, except for the flex, so I have made my template undersize. I think the Proxxon would do the trick.

True Alan, and it's really sloppy design on Dremel's part (both Mototool and drill stand), but in this particular case, black tape doesn't work. There is a lot of side force going on and when that bit hits the hard grain in the spruce, you can see the collet, bit, and drill stand move, even with the tape. The Proxxon has the bearing pressed into an aluminum housing.