Today I had a chance to pick up my repaired control lever for the transmission. I've attached a photo.
You can see by the thickness of the sleeve how much we had to mill out in order to reach enough original metal to support the new sleeve both on top and bottom. The sleeve was honed out just enough to give the bushing on my shifter the clearance it needed to work well.
Of note, using an original bushing the size is a bit larger, but the inside where the shifter inserts is worn enough to give it some slop.
Using an almost new bushing which is minimally smaller but not worn inside, there is virtually no slop in the system at all and it is a significant improvement from where I started. If I were designing the control lever, or thinking of another repair, you could likely make the sleeve taller and have it support the bushing even more as you go through the motions of the shifting.
In an event, an original part was saved and my first Austin-Healey repair project is done. I actually finished the fuel tanks sender already, but started the transmission first so it's the first one I undertook.
Thanks to Duane and Richard for the offer of parts. If anyone ever needs this part repaired in the future it's not that difficult for a machine shop to do over the course of a couple of hours.
Patrick