A zig-zag like this, is due to elastic behavior of the sled to triangular link to chains to beam to workspace.
It is more important at high center position where chain tension is higher and chain angles lower when the router gets closer to top beam.
I would recommend to make sure the beam does not flex. To observe that, attach a laser pointer on the top beam, pointing on a wall ideally several feet away. When moving the sled from top to bottom, any horizontal beam movement toward workspace center indicates a horizontal bowing where beam tips get closer.
Second, move the laser pointer to a nearby steady position and point it to the top beam tip face. Then move the sled from left to right along the bottom of the workspace. This reduces the previous bowing and shows the horizontal downward flex of the tips as the sled weight gets closer under.
Then the triangular link and chain clamps may flex too.
How stiff you need all of it depends on how much vertical force your router bit produces. When going from left to right, a vertical lift is induced, the other way around, it is a downward force. The deeper the router bit, a dull bit, a fast feed rate generates a stronger force.
Now this type of big wood chips is not homogenous, and that is likely to create vertical force variation along the path, creating a zig-zag.