I made a small test for acceleration and startspeed setting of the gantry but when you rotate the lines 90 degrees it can be used for the X aswell, probably:
you see two columns of 15 x 45mm engraved at 20% 500mm/sec and a scangap of 1mm in a piece of paper..
I set the acceleration of all axis to the max the controller can handle (50000). then you see what happens: on the left column you see beltstretch etc. I had to reduce the acceleration till the lines became straight (right column) for the gantry that was at 10000.
But my steppers are 3NM running at ~50V 3Arms coilcurrent (yes the get quite hot)
Running this columns takes you only a few seconds and maybe you can get the right values a lot faster. at least close enough to test it again on your material..
Hope it helps a bit

- Pattern.JPG (75.48 KiB) Viewed 2031 times
Oh and is your shift in one direction only? X?
can you also dump a picture of your user-settings-page?
BTW as you write that the cut-stitch goes highwire, I tested the stitch-pattern only (not the V's ) at absurd high values for acceleration 100000(onehundred-thousend) a startspeed of 50.000(fifty, which is the maximum you can enter) a max speed of 2000mm/sec and all values on the user settings page set to the max.. higher values are not accepted by the controller
I also set the speed to 1000 (it was 40)..
except for the beltstretch deformation (my belts are only 10mm wide, so not the best for high speed machines

) and a heavily shaking machine, the end of the line is perfectly aligned with the start.. even when I repeated it on the same position twice.... just perfect..
So I guess you still have to find the problem in loosing steps of your motor or a problem with your stepperdriver.. my system does it just fine, as expected..
Kees