The problem: the pulleys I ordered to drive the cut-off wheels have a 3mm shaft bore, but the 4" cut-off wheels I bought yesterday at Home Depot have a 5/8" arbor hole.
3mm << 5/8"
3mm is probably a little small for the shaft anyway, so I'll just use the existing bore as a pilot to center and drill a larger bore (1/4", if the pulley allows). Still not enough to fit the massive arbor of the cutting disks.
I don't have the luxury of a metal lathe to make a custom mandrel, so I start digging around online. There are some hole-saw mandrels that fit 5/8" arbors but they're expensive ($15+ each). They also have a hex-shaft, which could be a liability.
On the cheaper end of things, apparently there are drill/grinder mandrels (such as this one) specifically made for cut-off wheels with a 3/8" arbor hole. It looks like I can get 4" wheels with 3/8" arbor holes, so this looks promising. Oh darn, looks like I have to go back to the hardware store.
Ideally I'd buy a pair of mandrels and secure each shank directly into its drive pulley. No extra shaft needed!