Re the sloppy shift linkage:  I had the same issue on my LS.  In fact, when I checked the shifters on a number of other airheads, I found the same thing, and worse.  I don't know how much of the bad reputation these gearboxes have is due to this slop, but it certainly can't be helping.  The problem, it seems to me, is that BMW has specified a too-narrow needle cartridge for the shifter.  On first taking it apart, I thought, "Oh, good, those clever German engineers put a serious bearing in a vital spot.  I'll just replace my worn bearing, and I'll have a  slick-shifting Beemer. (An oxymoron, I learned)
Fully half of the available bearing area is taken up with seals. Â I thought of eliminating the seals and installing two bearings end-to-end, but two didn't quite fit. Â I ended up adding a brass shim (about .020" thick) on either end of the shaft. Â You may have to play with the thicknesses. Â Eliminating the end play helped quite a bit.
I'm still looking for a needle cartridge that is longer than the OEM part. Â It might involve boring out the lever, or turning down (or shimming) the bolt, and maybe some o-ring grooves.
Steve