The cable (round with a black covering) that feeds our electric range
has no markings that I can make out, but the breaker is a dual 40A, so I
guess the cable must be 8-3 (or bigger) + ground.

What is the approved means of securing this where it runs across the
joists? At present it has nails hammered in on each side and bent toward
each other forming a "two-part staple"! I am sure that this cannot be
kosher, but I can't find anything that is marked as being for cables
this large.

What should I be looking for?

Perce