Since the voltage regulator is a separately serviceable unit, it may have not been included with a replacement alternator. Earl has a point, it takes 5 minutes to pull it and look at the brushes.

Here is a possible way to test if the problem originates from the ACC system.
ABS light on and radio off is the result of low voltage. These, along with dimming headlights are the classic symptoms of a deceased voltage regulator.

Duplicate the conditions that gave you ABS light on and radio off. Then turn the ACC off (-O- button). Assuming the ABS light goes off, turn the radio back on, then turn on the headlights -bright- and the rear window defogger. If you again get ABS light on/radio off, your problem is outside the ACC system. Look harder for a poor ground, cracked wiring, possibly replace the voltage regulator.

If you cannot make the ABS light come back on with every non-ACC electrical gadget in the car turned on, concentrate your testing on the ACC subsystem.

If you have a soldering iron, before I replaced the ACC control unit, I would pull it and melt every solder joint on it to take care of any faulty soldered connections. (which is not uncommon as these cars age) Same for the OVP relay.