This reminds of when I worked for a carnival ride company. State inspectors would count the threads showing on various parts after a ride was installed. I believe the wanted to see two full threads.
If the rod goes all the way through (and I believe it does), it may be possible to turn the entire wooden handle on those threads until more are showing.
Another idea is to clamp it up in a vice, get a socket from a socket set, place the socket over the threaded end, and start tapping the handle down further with a hammer.
It may also be possible to combine these techniques. Put some turned force on the wooden part while tapping on it with your other hand.