95shaw,
I believe this fulfills the reversing requirements. I'm still trying to figure out what you mean by being able to always keep the 24V circuit live. When I originally sketched it (without solenoids) I had a battery shorted out. You can't have 2 batteries in series and parallel at the same time without one being shorted out. I don't want to pull my 12v from just one battery alone because it will discharge faster than the other and lead.
I could probably make 1 battery the up and 1 battery the down if I threw the stock winch controller in the trash, but I would rather not do that. Also, I don't think raising and lowering would have an equal drain on the batteries anyways.
You cannot use both batteries to get your 12 volt output (parallel circuit) while connected to get 24 volts (series circuit). You can get your 12 volts by center tapping as described and alternating batteries, with the 24 volts still available. The series/parallel switch accomplishes the same thing as your 4 solenoids would.
The point I was originally making was that the 24 volt charger would not charge the batteries evenly. (Overcharge one while not sufficiently charging the other).
The described method would get you a bit of the same, but is a compromise to pulling 12 volts completely off 1 battery. Batteries are never 100 percent equal no matter how you use them, so life is compromised somewhat anyway. This is also why you should never replace just one battery in either 12 or 24 volt circuits with single charging system.
Personally, I would keep it simple, by center tapping, and charging batteries separately.
FWIW, I use the hf 2500 lb winch to load my sportmod onto the trailer using single cable. I've loaded a 4500 lb tractor with the cable doubled up. Been using for couple years after my superwinch crapped out. Hf has come a long ways quality wise in recent years.
The $60 price tag makes it affordable to have a spare.
Add:
The circuit breaker size shown in your pic will give an indication of current draw by winch at full load.