I freely admit that I am out of my depth on this thread, but talking of squaring the plane cheek for shooting (look at me using the jargon like I know what I'm talking about!), wouldn't it be easier, and less expensive, to adjust the shooting board rather than the plane? Assuming it is out of true to such an extent that it affects your work, planing/sanding the wood the plane runs on seems easier than removing metal. If you get it wrong, throwing away a scrap of shooting board seems cheaper than throwing away the plane. I appreciate that everything 90° and true would be best, but if my plane falls short of perfection, I know I can happily make more mistakes on cheap wood than I can on expensive planes.
Have I just commited a heresy, or is there a sensible reason that the plane MUST be square, as opposed to having the shooting board specific to a particular plane?