Well I fixed my seat "movement". Turns out it wasn't the seat, but the plastic on the side buckling I suppose, which felt/sounded like the seat moving. I bought this:
https://www.amazon.com/gp/product/B01M1EQHDO/ref=oh_aui_detailpage_o02_s00?ie=UTF8&psc=1
Cut out two strips about 1.5"x3", glued them back to back and shoved them in the plastic gap just in front/under of the horizontal seat adjuster. Voila, solved.
If anyone else tries this, I'd be curious to hear if it helps.