Since I am going to have to drill freehand, maybe I should go with a
5/16" hole, instead of the 21/64." If there is a slight out of round,
my thinking is that - the cast iron being soft - the tap will
compensate.

The taper on the tap looks tapered enough to fit into a 5/16." Any
objections to this plan?

If this is something I could not afford to botch, I'd drill undersize and
invest $10 in a reamer (or perhaps 2!) to bring the hole size up to final
requirements.

Jonathan