[Suicide Junkie]

If it was a real black hole, then it would only pull as hard as a normal star. (ie. zero movement towards center)

For example: If we somehow accidentally crushed the entire planet earth into a black hole, the event horizon would be the size of a marble (~1 cm) Satellites in orbit would remain in orbit, since the mass of earth hasn't changed (and hence the force of gravity)

Since a star's gravity has no effect on ships, a black hole's gravity should have no effect on ships (unless it is truly massive like 1000x the mass of the sun).

At the center it should do infinite damage (ie. no escape), and do heavy damage at ring 1 to 3 (from the accretion disk plasma & radiation)

Perhaps we should add radiation/heat damage in normal star systems? If you stray too close to the sun for too long you burn up. Say 200 damage per turn in the star's sector.
Only the highest tech armor should be able to take that without being destroyed, but even a handful of armor IIIs will protect your ship for a turn or two.