I am using a
Pondmaster pump, the Mag Drive 18. It has no motor to ever wear out. It is a sealed electromagnet that spins a steel shaft with an impeller on the end. The model I use pushes 30 GPM, but there is also a bigger one. This one will keep up with extracting heavily flooded carpet after you pump it down for extraction.
This inverter powers it and connects to the TM battery. Yes, this inverter is overkill but it is a complete 15 amp circuit in case you need additional power fro something else. My LP heater is also 110 VAC, but only uses 2 amps.
The pump sits on the bottom of the recovery tank and uses a sump pump float I got at WW Graingers. Inside the tank there is also a 3/4" check valve.
I have not had to physically dump a recovery tank in way over a decade which is really nice when out working all day.