Well I tried it! Bought a 5-speed drill press at Harbor Freight for $65 + tax (free shipping with a coupon code I found online). Add a stainless steel bowl, some pipe insulation, duct tape, and an old nut & bolt I had lying around, and the ball spinner is working perfectly for less than $80. The second lowest speed seems to work best.

Photo here: Ball spinner photo

I guess it remains to be seen how long it'll last. But after resurfacing five balls, it's already paid for itself.