In my case, I was assembling an electric fireplace and found that the factory had missed installing 2 critical inserts. I measured the thread size of the screw that was to thread into the inserts, and the depth of the hole in the wood piece. Fortunately those were the only 2 measurements I needed (although I also measured hole ID, hex wrench size, etc).
For the shift knob, I'd start with the thread size on the shift lever. I have a feeling that's where my suggestion will fall apart -- it's likely either British or UNF, and I think these inserts are only available in UNC (though if it's Whitworth thread, UNC might be close enough).
Then measure the depth of the hole in the knob to be sure you don't get one that's too long, and measure the hole ID and knob OD at the base to be sure you don't get one what will cut threads right through the knob, or a flange that sticks out too far (though you could grind the flange OD down to match the knob; you could also cut down an insert that's too long).
The E-Z Lok has a flanged end so it looks like an oversized, countersunk screw. That's probably not the style that would suit this installation. Creepily, I got a targeted ad in my email this morning from Global Industrial for E-Z Knife brand threaded inserts. Point being, there are more options out there. I'm pretty sure that Ace, Home Depot, Lowe's, and the rest carry some, just not the style/size that I needed for my project.
A Heli-Coil insert, or even better a solid insert like a Keensert, might also work. Same concept but designed for installation in metal (and available in UNF and possibly even BSW/BSF sizes). You would have to clean out the stripped threads and tap fresh threads for the insert, but at least the nut would be bearing against the solid metal of the insert instead of against wood. The only stress that the wood will have to bear is your hand moving the shift lever.