You would need a float switch in the 2500 gallon tank. You don't need a valve in the tank. The float switch will control the pump, probably through a contactor or relay.
I would want to look at the curve for the pump, and know the depth to water in the well, to determine if the increased flow you would get to the 2500 gallon tank would overload the pump.
You should probably have a Pumptec or other device in the well pump circuit to protect the pump if the well from being pumped down too far.
You would need a pump from the 2500 gallon tank to the pressure tank. I suspect that the Davey pump might be inadequate. I would have to see the curve for the pump.
There would be another float switch in the tank to protect the Davey pump (or another) if the 2500 gallon tank runs out of water. I will refer to the Davey pump but it may not be adequate for the service.
Your pressure tank would be supplied by the Davey pump or its replacement.
You can connect a chlorinator to the well-pump circuit to add chlorine (diluted bleach) to the tank. That is a good idea because those tanks can be contaminated.
The hydraulics would be:
Well pump => 2500 gal tank => Davey pump => Pressure tank
with the pressure switch on the pressure tank controlling the Davey pump.
No valve between well pump and 2500 gallon tank. You will need a check valve on suction or discharge side of Davey pump to prevent backflow from the pressure tank.
You already have a filter for the potable water. I would not add another. The iron will probably be oxidized in the black tank and you may get more iron precipitate in the filter.