The problem is that the two thread sizes are too close in diameter to use either a HeliCoil or any type of bushing to be used in-between the knob and lever.  This is complicated by the knob having fine threads and the lever being coarse. 

The threaded and tapped extension suggested by 62Cooper is a good method whether you use a bolt for a starting point or not.  You could select a bolt or rod long enough for you to bend it "backwards" to make a copy of the period accessory shift knob extension.  You could also try Dan's suggestion of filling the knob with JB Weld and then tapping it to size once cured.  However, the resulting assembly will only be as strong as the threads in the epoxy.

 

I would try to find the most pliable material possible to put between the shift rod and the knob, to reduce vibration + noise.

What I would do is get a bolt that fits your shift knob, and drill and tap it to the threads of the shifter, then screw it into the knob with locktite, then cut the bolt off. Send me the shift knob, and tell me the size of the threads on the shifter, I'll do it for ya for free. Just pay the shipping.

I've found that a short piece of plastic or PVC tubiing makes a perfectly functional adapter. That's how I used to make beer tap handles into shift knobs.

You might get a helicoil (for stripped threads) or something similar to work.

Or you could get a piece of tubing, thread the inside on one end for the existing shift rod, and the other for the knob, putting threaded stud or cut-off bolt in the tubing. Look for a piece of 3/8" I.D chrome plated tubing in the plumbing section (or under the bathroom sink). A short piece could be bent once installed, or left straight.

For the hexagonal look, seek a coupling nut and you could re-tap one end - it doesn't take much to hold a shift knob on.

Or just fill the knob with JBweld (a soft metal version) using a wood or plastic dowel as a soft core, and re-tap. Or just grease the shift rod before pressing the JB-filled knob on. when cured, remove, clean off grease and reassemble.

I have a porcelain door knob that's about 115 years old for a shift knob, so what you're asking should be easy-peasy.

 

I have a shift knob with thread size 3/8"-24 thread that I want to install on my mini does anyone knows if someone makes a adaptor? I measured the thread size on the the mini and it looks to be 5/16-18.  I got the measurements by taking the knobs to Homedepot and trying them on their bolt gauges.  A bent extension/adaptor would be cool.  Thanks