So, IIRC you DO have two strings of 370 Ah batteries, but are charging them individually, perhaps via a battery switch ...
YES, am unfamiliar with the Schneider SW inverters. Many Inverter/Chargers have charge current settings that are in AC amps, not DC ... perhaps the SW has either, both or DC only, dunno.
When you said, "I'm using the charger to bring my batteries up to their finishing stage - in the 90's", assume that the 90s is the approximate SOC.
Schneider and some other inverter manufacturers have a provision for using a Bulk voltage that is different from the Absorb. Personally, have always set the Vblk and Vabs the same. You need not worry about a good Vblk on the Classic, as the Classic does not need a Vblk setting, and will produce the maximum amount of power available from the PVs. The Vbat will increase until the Vabs is reached, THEN, a Constant Voltage stage begins, where the Absorb voltage is maintained as a constant, and the battery Acceptance will cause the battery current to taper.
46 Amps DC is probably a fine current maximum for Bulk and Absorb when charging a single string of 370 Ah batteries.
With "the PVs disconnected", am surprised that the Classic would read "Absorb", and not Resting.
From what you have stated, do not know just what is the setting that causes the 29.6 volt reading when charging from the SW. But, most likely, the batteries are cold, and the BTS on the Schneider should be increasing the Vabs (or Vbulk) to compensate for a lower battery temperature.
If you DO lower the Absorb Amps on the SW, then in early stages of Absorb, the battery voltage should drop below the Vabs voltage, and revert to Bulk, until the battery Acceptance drops to the DC current that corresponds to 37 A DC (or whatever you have as the Max setting). Then the battery voltage will increase, in time, and still reach Absorb ... it will just take somewhat more time.
Regarding the relationship twix Max charge current setting in the SW, and battery voltage, the relationship is a direct one (NOT inverse) -- reduce the charge current available, and the battery voltage will drop, when in Bulk, and when in Absorb, only when the battery Acceptance is greater than is the DC current available ... if this makes sense.
SOC readings on any battery monitoring device are approximate. The decision on how long into Absorb should generator charging continue, is a very grey area. Would run longer into Absorb, if it had been a number of days since a full charge, especially, if the following several days were forecast to be relatively poor solar charge days, and so on ... it all depends. But this is a good question, as much of the Absorb stage is not a good use of fuel, if good sun might be available later in that same day, or on the following day ... depending ...