I think there will be a torque limit (from the stepper motor) which can be applied to the leadscrew, otherwise the bearing will want to jump over the teeth. Depends on the spring preload holding it against the teeth - higher is better for this, but then more bending load on the leadscrew which is less good. This effect will probably be the determining factor in the success of this idea, but good thinking!

Better tooth engagement from a brass insert, as you suggest, might help although there will still be a limit - you'll have to see how it goes. You might be able to arrange a locking up nut so that when the spring tension is developed you can lock it off at that position. Of course this won't compensate for small variations along the thread, but might be a fallback position if it keeps jumping.