138mm headtube.
165mm steerer tube (threaded, measured with the straightedge at the bottom of the tube, right up against where the bearing race would touch the crown).

Will a Gripnut headset help me, or do I need to go with a different fork?

a gripnuts minimum stack is 37mm. seems like you're 10mm short.

Damn. I knew people used them for forks that were too short, but I didn't know exactly how short. I couldn't find any specs on their stack height. Thanks all the same.