First, welcome to the classic & vintage bike forum.

If you can somehow tell that the steer tube is 22.2mm dia, why not use the same way to measure the crown race diameter?

If it's much over 37mm stack height you'll get the final result with the lock washer and spacer shims, even if you get a headset with a short stack height.

I think most of the 80's Miyatas are ISO 26.4mm crown races, and the 700 series you have is from a better model line, which makes that more likely. I think you can get Tange Levin from online retailers for ~ $19 +shipping.

The tools are another story - the crown race extractor can be $60-150 and the installer/setter $25-75. LBS might be the way to go to pop the old one off the fork and put a new one on.