Theoretical measure of distance to black hole?
Yes. If you could spatially resolve a black hole and measure the redshift of radiation at a given angular radius, then that would yield the distance to the black hole.

This works because the amount of redshift depends on the ratio of radius to Schwarzschild radius, but the latter is known if the mass is known. Thus the redshift yields the radius. The distance is then given by the radius divided by the apparent angular radius.

There will be complications due to gravitational lensing and any orbital velocity around the black hole, but this does not stop it working in principle.