Cuprajake
Some (one) answer. I pulled the piston again and measured the white gasket with the extra shipped with the machine. Identical.

However, I flipped over the piston and noticed the very slim plastic gasket/spacer beneath the springs was badly split:

That would be a candidate for the recent jerking motion of the lever on shots. I don’t see a replacement with the shipped supplies, so I’ll likely need to contact acs for a replacement or dimensions so that I can order closer to home.
I’ve never unscrewed the spring assembly bolt, so I’m not sure how this gasket tore so badly or how to avoid it in the future. More mysteries.