Like this?
That looks ridiculously flexible to me so I'm not surprised that the piece got dragged sideways by the cutting forces.
I see from the previous pictures and video that this is your usual clamp method (external perimeter clamp or corner screws, with stock only just bigger than the piece). Are you using something sticky under the workpiece as well?
I'm surprised you don't have more accuracy problems, even with delicate DOC and speeds. I'm no expert on clamping because I mostly use vacuum hold down, but when I do clamp I am very wary of flexing. Where possible I put screws through the workpiece.
If you are going to experiment with more aggressive cuts try using larger borders on your stock. Even better use tabs to retain the stiffness in the stock.
Another tactic would be to use aggressive cuts followed by a shallow cut at full depth, eg 3 cuts of 0.0.22" followed by 0.10" , take all the parts down to eg 90% depth before cutting any of them free.
I've only just started using 18mm birch plywood. One tactic I've used for a clean cut is to score all the cuts using 1mm doc with my 1/8" downcut bit, and then do the serious removal using my regular 1/4" upcut with 3x doc 6mm. I'm sure 2x 9mm doc would work too.