I have some T-track hold downs that slip between the metal frame edge and the wasteboard. They are pricey though and do not fully solve the clamping problem on their own. The stock has to be supported well enough to withstand downward (edge of the stock) milling forces and, as you mention, square to the X axis.
I did a few projects but haven’t iterated to the next refinement of the setup. If I do though I may try to have some way to shim left/right other than slipping in bits of paper or other shim material. You can verify square pretty well by dropping a v-bit at zero Y and max stock X (or somewhere well east of zero X). Or if you have a touch plate you can find zero at both ends, compare Y zero, and shim until you are satisfied that it is close enough.
How much you get into squaring it depends on what you are trying to do. My metal frame and X axis are probably 1mm-ish off parallel through the whole span of the machine.
Update: Link to setup Carving on the edge