Mustachianism is about putting your money towards things/experiences/etc that you value. If a dishwasher is something you value, just get one and stop worrying about it. $700 is not an outlandish dishwasher either, and quite frankly I would never spend money on a cheap one as they are usually way louder, use more energy, and are often uglier. Now, if you were talking about a $2200 Thermador or Miele I'd have to punch you in the face, but $700 is pretty typical, let alone for a special sized one.
That all being said, if you aren't exaggerating when you say you're a couple mm away from getting the clearance you need, I'd just use a belt or orbital sander and sand the subfloor or underside of the countertop down to make it fit.