This is almost certainly a transient problem.
The voltage regulator (inside the brain box) takes a peek at battery voltage once per ~100 ms, (milliseconds) and takes ~1000 ms to adapt the alternator(s) to a step change in current demand. There's no speeding it up in the field; it would require a major design change, which could only come from the Glass House.
A brush-type DC motor draws a huge inrush current, which reaches its peak in 1 ms or less. It's not possible to speed up a voltage regulator enough.
Reducing the size of the plow feed wire isn't feasible unless it's oversized to begin with, and either won't have enough resistance to effectively damp the current spike, or will have too much resistance for the pump motor to run efficiently. (I suppose you could use a resistor in a soft-start configuration, where the resistor's in the circuit for the first 0.1 s, then is replaced by a relay contact closing after the motor starts turning)
Adding an inductor in the plow feed wire will help level the inrush current without affecting steady-state motor performance.
A supercapacitor is a better choice than a third battery. They're smaller, lighter, contain no acid, don't lose power in the cold and will never need maintenance or replacement.
There's probably a wide variety available through extreme car-stereo channels. Likewise high-current inductors.
I've been trying to wrap my head around the advice in the bulletin and it makes very little sense. All I've come up with is that running the alternator(s) at a higher-current condition might make more load dump available. But relying on load dump to hold battery voltage up is a pretty big kludge.
Likewise "11 volts". It's absurd to think that automotive electronics wouldn't function just fine at 11 volts. It's much more likely that the battery voltage drops to ~6 volts for a few milliseconds and somebody measured it with a slow-responding general-purpose voltmeter.
One final thought: Is the oil the right viscosity?
Hydraulic pumps work best with a viscosity of about 20-60 mPa·s* (milli Pascal seconds, aka. 20-60 centiPoise) But hydraulic oils are rated & labeled at 40°C. (104°F) If the actual oil temperature is going to be closer to 0°C, switch to an oil that has the optimum 20-60 mPa·s viscosity at 0°C
* Be sure to look up the specification for the specific pump in use.
On a related note, has anybody ever heard of heated shock absorbers? I'm getting really tired of being bounced around like I'm in a rock crusher, merely because the oil's cold.