Well, actually if there is less string when the sled is in the corners, then tension would increase…
Looking at the diagram below, the maximum force would be applied at when the sled is at the top left (close to the motor) because that’s where the chain is the least. This is where you “calibrate” the stretchy string. You attach the string to the sled when its in the top left position, wrap it around the bottom idler up to the sprocketed spool and take up all the slack. You really want this taut at this position. As the sled lowers, it will naturally feed out more stretchy string and the force will decrease, but it will still provide tension (how much depends upon how much string is unspooled and the elasticity of the string). When the sled moves to the right, more string will be spooled-out and therefore it will stretch more to the point that the tension is really low when the sled is on the far right.
The amount of force applied will depend upon the elasticity of the string and the diameter/gearing of the spool. Finding the right combination will be the real challenge… assuming this works.
Additional thoughts… First, the sprocket for the spool may cause issues leading to chain slip (since it will want to push chain back toward the motor.) Second, I don’t know how chain sag calibration would be affected by this… but since it’s not consistent across the entire surface, it probably won’t be good.