I kind of like the old-style spindle-back Windsor chairs, but only some of
them come with bevel-cut (thus planar floor-parallel) feet; others have a hard
steel button in the middle, or just hold the turned leg end angled against the floor.

Without drilling into the center of the feet (they're tapered, it's hard to jig up
for a coaxial bore) how can I attach feet that spread the pressure so my floor doesn't
show tracks?

Most gliders either take a center-spike connection (nail into endgrain: not nice) and
have small tilt freedom, so won't suffice.