Re the support for thin stock/non-flat/slipping, how about using a vacuum bed as a moving table with the edges only (top, bottom and sides) engaging the rollers ?
A length of 1" wide emery cloth along each of these faces will hopefully provide sufficient traction.
For the table, I propose to use a hollow door for its size/weight/cheapness.
This is what my own #3 machine will use, if and when I get the #2 finished
John