Looking at the pic of your platter, it definitely doesn't seat on the bottom.
It matters. A great deal of flutter in a test tone is arm/cart behavior. If the cart isn't set up right it'll be worse. Also want a healthy cart.
A way to figure out how much the test record I used is a factor might be for me to re-record the same tracks with different turntables... Not sure how much trouble it is for you to run the analysis though.