"...In this case, I would run #10 all the way from the panel to the conduit boxes serving each machine (see another, related thread on making one's own "bus way"). Then #12 from each conduit box to each machine's safety switch."
A minor point if I may. Even if the machine's overcurrent protection, at the machine, is sized for 20 amps, the conductors
from the conduit box to the machine, still need to be sized for the *up*stream overcurrent protection. In this case
they'd have to be all number ten, except down stream of the overcurrent protection (rated 20 amps) inside the machine.
Actually, section 240 allows "taps" from a "feeder", and puts no restriction on the wire sizes that may be considered a "feeder" (i.e. no limitation to 1/0 and above or some such). While it may be expected that it would not be used for small wire, that is not prohibited, and the definition of "feeder" puts no restriction on it either.
The "tap" must be no longer than 25 feet, must be in raceway (conduit, etc) , must have ampacity no less than 1/3 the "feeder", and must terminate in circuit protection rated for the tap ampacity.
A fused safety switch at the machine would meet that requirement, IMO.
So for a #12 "tap", limited to 20A, the "feeder" could be, for instance, 75C rated #6 protected at 60A. Then, #12 could be tapped off of it and run in EMT, IMC, or RMC to 20A safety switches on the wall at the machine.
You could NOT, for instance, use NM cable for the tap, but using it probably would already violate the "exposed to damage" clauses, so you wouldn't do that.