"winch motor powers pulley system"
Is cable being taken up on the winch, so more turns means less mechanical advantage?
Or just one layer on a reel, which is how the spring-loaded take-up works for mine?
There's one solution - spring assist. Although it will assist less the higher it gets, because unlike my garage door tracks, your bed keeps going straight up.
If a 2500 pound winch has trouble with a 300 pound load, appears it is really being starved for power. Unless, the winch was rated for how heavy a vehicle it could pull on flat ground.
Set up a block and tackle that cuts load to 1/2 or less?
24/12 buck converter - Supercap?
I've heard they're being put in car doors to power the window motor, cheaper than fat enough wires. (I would use boosted voltage if I designed it)
Two small additional 12V batteries - series with system to charge, switch to parallel for 12V operation of motor.
Two, (identical) 12V winches wired in series, each taking half the load.
Tap off 1/2 the battery bank for 12V. Make a switch so you can use one 12V battery one time, the other battery the other time, to balance discharge.