The other day I saw his 'ible again and realized that I could make something similar to it using an old woodturner's trick. Actually, I think the reason I tried it was because of his comment that the methods he used were somewhat dangerous and he didn't want people getting hurt. So, naturally, I saw it as a challenge to make one without killing myself.
WARNING and all that: Use appropriate caution and attention to safety when working with power tools. Always know what your tools (and you) are capable of and don't make things do what they're not designed to. If you're unsure of your materials' structural integrity, please, at the minimum, wear a face shield. And it goes without saying (and yet here I am, saying it), ALWAYS wear safety glasses.
Step 1: Prepping the Wood
You'll also need a glue block, I'm using a piece of 1" x 2" pine here because it's what I had, but you should use something that doesn't splinter very easily (maybe poplar or whatever else you have on hand). I had problems with the osage coming off because the pine splintered where the glue line was.
Cut a section of the glue block material a few inches long and mark the center. Use hot glue, CA, or something else you trust to glue the puck of osage to the block, trying to keep it as centered as possible.
Now remove two jaws opposite each other from your chuck, and mount the block assembly.
Step 2: Turning the Outer Circle
I turned a shallow dome, sanded through 400 grit, used EEE (a wax that contains particles of tripoli compound, a micro abrasive) for a nice shine (get it? EEE - triple E? ...ahem. sorry), and finished with Renaissance Wax.
Step 3: Turning the Inner Circle
Step 4: Drilling a Hole
No matter which way you do it, since you're most likely gonna be drilling through rounded surfaces (i.e. not perpendicular to the drill bit and thus likely to wander), I'd recommend inserting the bit almost all the way into the chuck, leaving maybe 1/4" sticking out, and tightening the chuck loosely so as not to damage the flutes. Carefully drill a shallow hole just to start it, then place the bit where it would normally go and drill the rest of the hole.
Step 5: Parting Off
Step 6: Other Options
As usual, be careful. Keep in mind that the bearings in drill presses are not meant to sustain sideways pressure, so I don't really advise you do this too much. I don't know whether or not this will work as I've never tried it before, so use at your own risk. If in doubt, just find a local woodturning club and I'm sure they'd be happy to let you use one of their lathes.