We have a large pressure tank (80 gallon I believe). If the power goes
out when the tank is full, we're fine. 80 gallons will flush a lot of
toilets. Unfortunately, the tank is rarely completely full when the power
goes out and this last time it was nearly empty when we lost power.

Not clear why this has to be the case?
AT 45 PSI, you should be able to keep the tank 2/3 full of water.
If that's not possible, you've got a flow rate problem and need more
storage. Will take more energy to pump against higher pressure, but how
much?

For big water storage, you can pressure it when needed with CO2.
When there's no emergency, you won't want the CO2 tank going to waste.
I suggest a fridge with a keg in it as a resting place.
When the power goes out, just drink beer until it comes back on.
Problem solved.

My favorite solution to a power outage is the well-deserved nap.