Knowing by whom/where it was made could settle the issue.
9/32-24 is a thing,
You are quite right. It turns out that vintage Stanley planes had one bolt with that thread. So I made a $5 purchase of one bolt on ebay.
Problem solved.
Yes, chase the thread and have done with it. What sort of die head is it?
Those dimensions are real close to being an M7 x 1.0 thread.
helicoil