This improves our granularity to the range I'm interested in, but at
the expense of maxing out a CPU.

Remove -DSPIN_OK from the CFLAGS line in the makefile if you don't
want this behavior.  Note that this only happens if you're attempting
sleeps of < 1second.  If your sleeps are longer than that, the code
will just use the 10ms timers and figure you're getting time target
hits within 1% anyway.