You can clamp the rollers on the long/mid arms without feed dogs and get the straight stitching you are talking about. If you want a square grid it would mean going across the quilt left to right, unload it then re load it the other way. If you wanted it corner to corner you'd have to load the quilt on the diagonal.
I had a domestic on a table top frame that I only wanted straight stitching left to right, not up and down and this is what I did to keep the stitching even.
If there is a will there is a way......