If accuracy is not important, why use expensive ballscrews? Ballscrews have very little friction so if motor power fails the load will fall uncontrolled. Singly-threaded trapezoidal leadscrew ought to avoid that danger, although require more angular velocity for a given linear speed.
Some sort of leadscrew is probably good for this high load and low speed requirements.
Three rather than four leadscrews might be enough, saving cost.
Using one motor and a belt to distribute drive to each leadscrew is also a possibility, again saving hardware,
but the torque requirements might be an issue depending on the pitch of the leadscrew.
Simple DC gear motor with encoder is a possible alternative to stepper(s).