Thank you for the link, but I think Richard is right. The 15mm mentioned in the adapter description refers to how long the adapter is, not the thread (which is 5/8-27 to 3/8-16).
I thought of retapping the female 15mm thread at the base the of microphone clip, since all the male counterparts (microphone stand, boom pole, etc.) are the standard 5/8-27 already.
But the microphone clip came with its own set of adapters: one for a regular hot shoe, one for a mini hot shoe, one for a gorilla pod-type set of legs. So if I retap the female end of the microphone clip, I cannot use any of the accessories that came with it.
I was hoping someone would manufacture a 5/8-27 to 15mm converter that I could use.
Alternatively, I could get this thread saver (https://www.bhphotovideo.com/c/product/1076269-REG/latch_lake_thsvr_5_8_thread_saver.html) and retap the male end of it to 15mm. But by the time I purchase the thread saver, plus a die, plus a die wrench, I’m better off buying a different microphone clip.