A common cause of shifter looseness is wear on the 2 bell crank balls, or the ball at the lower end of the diff housing selector shaft.
These are now NLA new.
I have had success with building these up with `toolcraft' or similar hard facing electrode, then sanding them back to size. Measure with a micrometer and sand carefully.

Agreed on the excellent post, although I have the same dilemma with the remote shift.  Mine has trouble in the 2-3 upshift and it feels as if there is a gate there and difficult to get into 3 while "at speed" and wants to drop back into first which can get exciting!

I too have the KAD quickshift and it seems like a well made unit but I still have the original gearstick so will try that to see if there is a difference.

All knuckles line up correctly while in neutral, even referenced a helpful video on the gearbox that was put together by our host.  I suspect wear elsewhere (no pun intended) which will probably happen at teardown time.

Excellent follow up post.

In your Mini with a remote type gear change it is not always just one part that causes shifting problems, it is the sum of the parts and the wear therein.  Fitted to all mini gearboxes up to the introduction of the rod change the knuckle was used.  Composed of two parts - male and female,  The male knuckle 88G224 fits into the female 88G223 which is now obsolete. So the female of this set is now listed as obsolete, NLA, CWE, or however you want to say unobtanium.

Doing a Google search on 88G233 and looking at the images you will note that there are two different images for the same female part number, with the main difference being a little raised area that can be drilled and tapped for a grease fitting.  My Cooper ‘S has this type of knuckle with a grease fitting on it.  I also believe it has a spring and a nylon cup internal.  As I can’t find a reference or a parts breakdown does anyone else have this type of linkage?

 

     If you have trouble getting the car into gear it could well be that one of these knuckles or both have worn.  (from description of 88G224)

     If you put either back in offset by one spline or more, your shifter ends up with some really loooooong throws. (credit Dan Moffet)

     Check the pinch bolts that hold the nuckles to the shafts, there should be no play between the shafts and the pinch bolts in the knuckle. (tighten if necessary) (credit Checkler)

     Another source for poor shifter response are the bronze bushings in the differential cover.  There is a grease nipple that feeds grease to both (one above and one below) I have been told the bushings are available at Lowe’s (I couldn’t find them at my local Lowe’s).  Replacing them can make a good bit of difference in the slop while selecting gears.  (credit Spank)

     Next look at the remote shifter control shaft (the part the female knuckle bolts to also NLA) for wear.  Then there’s the bell crank and the pin it sits on.  Now we look at the remote shifter itself.  Check it for cracks, look at the primary remote control shaft for wear on the “fork”, I have even seen the case modified with a grease fitting as well as the damper retaining cap (and plunger) being modified for a grease fitting.

     Look at everything from the gearchange lever to the primary shaft lever, you might even change the nylon anti-rattle bush (or put in an aluminum shim – soda/beer can)

     ,,, and once you get past the wear, there’s always the option of a “Quickshift”.  While I found it took a while to get used to, I wouldn’t be without mine now.  (credit Ian)