Well, since the spring force increases as it gets stretched, you need enough spring tension too keep the motor from skipping steps at the top of the stroke. That may turn out to be close to neutral at the center of the stroke. I haven’t done any testing to see.
There is a spring type that applies a constant force vs. an increasing force as it gets stretched. That would be a better option for this application but probably not worth the hassle of redesigning to make one fit.