Sorry for the delay in this answer - I was out of town for the weekend.
nortonden wrote:1) B marked “suitable for use as Service Equipment “
Very good, that means that the neutral "can be" isolated from ground, and, in fact, probably means the neutral
'actually is' isolated from ground but is bonded to ground by either a ground bonding strap or a ground bonding screw, removing the bonding strap or the bonding screw will now allow the neutral terminal bar to again be isolated from ground (isolated from the enclosure, which is where the bonding strap or bonding screw bonded to ground).
2) 4 insulated conductors feeding regular panel
Also very good as that is what is required to allow the neutral to be isolated from ground. Now check this: 1) the grounding conductor is attached to a terminal bar which is attached to the enclosure and grounds the enclosure, making the enclosure ground; 2) the neutral conductor is attached to a terminal bar which is isolated from ground by being mounted on plastic supports which isolate (essentially insulates the neutral terminal bar from ground); 3) that there are no bare grounds on the neutral terminal bar; 4) there there are no insulated neutrals on the ground terminal bar; 5) that there is only ONE neutral conductor per terminal in the neutral terminal bar; 6) that the number and size of the conductors in the ground terminal bar match what is allowed on the label.
3) Neutral conductor in 2) has properly marked insulation
Good, otherwise it is not insulated, just "covered".
125 amp main breaker at this (former service equipment) now panel receiving hots from 125 amp breaker in new service equipment.
That is fine, the 125 amp main in the panel is simply a "panel main" and is an additional level of safety, just not a requirement (but I prefer to have a main in each panel as it does provide an additional level of safety, and remember, "code" is simply the "minimum" one is required to do, anything above and beyond code is even better).
If you clear me to isolate grounds and neutrals to get the panel safe and correct, ...
That is what is REQUIRED, yes - the neutrals are required to be isolated from ground in that panel as it is no longer service equipment.
I’m considering adding an additional “floating “ (sic) neutral bar wired to original neutral bar and an additional ground bar wired to original ground bar to facilitate picking up the shorter grounds and neutrals and avoid the butt splice wire nut controversy
THAT is a problem as you are only allowed to add terminals bars into the panel if allowed by the manufacturer on the listing and labeling, and I doubt that is allowed.
“Separate equipment ground” does this mean a driven ground rod connected directly to panel?
No. What that means is that you have a insulated neutral conductor with a separate grounding conductor, which could be insulated, covered, or bare, and that grounding conductor is simply officially called "equipment" ground, and it needs to be (as stated) "separate" from the neutral.
Came upon a rebuild of a Hurricane Katrina house in which the “electrician” had installed a 125 amp service entrance with neutral / ground isolation capability, comingling grounds and neutrals, but had overlooked the need to supply electric range, cook top, hot water heater, and strip heaters.
Thus new large service equipment was installed for these loads and now also feeds the (original SE) now panel via the above described feeders.
Unfortunately, that is not at all uncommon. What you are lucky about, and is usually also missed, is that the conductors which are now feeders (were 'service entrance conductor' originally) typically do not have a separate insulated neutral and a separate grounding conductor, which means that (usually) installations like yours would need the feeders replaced. From your description, though, you do no need to do that.