Well, I've gone this far ....
The wood handle also a very tight press fit. There is an ~1" piece of tube stuffed into the handle that mates to the half-notch cut in the end of the tube.
Spikes on the inserted tube lock it into the wood.
To get the "gears"

off the spiral bar, a smooth cap is threaded on the end has to be removed.
At the other end, pull back the collar that releases the bits and there are two flats on the shaft that will accept a very skinny 3/8" open end.
I'm not going to mess with the chuck.
