I had same thing with my stock x carriage. After much trial and error replaced with surstepr drivers and problem went away
I still after 20 prints had bad circle problems and skipping in x-y as well as a x shift constantly caused by the z rod. Same spot every time shifts to the left and comes back in. Makes a hump on the side of all my prints.
So after my last failed y skip print. I pulled the carriage off and replaced with linear bearings, new polished rods in both x-y and printed new x-y carriages as well as but bearings in place of the bushings on the rear Y shaft. I was going to add the additional bearing block but the stock rod is so rough I couldn't jam a bearing that far over even with dremel sanding the rod down and it is 6mm not 5mm. SO weird but all the replacement items are 5mm for the pulleys but I can not source a polished 5mm rod just 6mm
So long story short.. the bearings were huge difference in free motion. i can push the right side, non driving, of the x carriage and the whole x carriage will slide on the y carriage effortlessly and without any yaw front to back from the other side like the SD one does very bad.
I know you might not want to make those changes but the driver was a must have fix if you have y problems because no matter what you do mechanically the driver will be the problem, it is an easy fix/swap and cheap like $12.
Now just along the bearing g upgrade, I did see a much sharp x-y resolution in my print and the noise and clunking went away (almost) still some slop in the bearings sitting in the carriages but x-y look good but I did still y skip after all that. So I found the belt tighten tension was key. and I missed that after install a few times. i recently tighten down and tighter then before because I can with the bearing. I also increased the speed too
So i backed speed to pre bearings, adjusted again and looks super clean. Now I suspect that even with bearings my surestep current is low since it can over accelerate now and maybe slips or overshoots more the skips per-se so I will play with more current on the Y, and acceleration values (which you can turn down too)
sorry if this is not a full answer but just insite
SD2 owner- Surestepr, filament holder,QUBD servo and heaters, glass bed
Print for fun and for parts for my sports cars
current car is 88 IROC