That's what I have done.
For squaring, I mostly don't have a problem because I have been using stock that is larger than what I am cutting, so the machine can do that. On the surfaced board I have on top of my MDF, I have cut dowel holes. I then put matching holes in my stock to make placing and flipping it easier.
One thing you could do is to use your machine to cut a perfectly straight and square rectangle of stock, and cut a hole in each end just large enough to tightly fit a dowel. Then glue some dowels in. Any time you need a square edge, you can just make matching holes in the top board (the one you have surfaced), insert your piece with the dowels, then place and clamp your stock against that.