Laser shifts by 1/4 inch in the middle of the cut

Yeah, that looks like something mechanical. You need to inspect the belts, the wheels, and the tracks closely. Make sure there is no debris on any of it, and that the belts are fairly snug and clean. (Resin buildup on the beds and wheels can cause that to happen - the belts will start to slip.)

If you need to clean the belts and wheels, you can read through this post to someone with a similar issue:

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