OK465:
Though the viz mins are aircraft speed category related, the real consideration as far as how challenging the sidesteps are to fly from closer in and down lower is not only the aircraft speed category, but the roll inertia involved.
I have FAA source documentation back to 1998. The earliest change I have is 2001 where the DAs are the same as today, but the RVR was 6000.
I was based at LAX from 1964 to 1990 and never recall sidestep minimums like these. I did it a few times but in basically VFR conditions and at least 3 miles out.
If someone actually does it today at these minimums I believe sooner or later a fireball would be the result. Sometimes the FAA is just plain nuts.