There is a very simple way to fix this, it's rough and ready, but it's quick and will be a lot better than what you have.
I'm assuming the carby is out of the vehicle and on the bench. First how bad is the slop in the bush and shaft, again i'm assuming it's pretty bad
Remove butterfly shaft from carby and clean it up as much as possible. in a lathe with a fine file and emery cloth, make sure it is parallel along its length. Clean out the holes in the carb body. clean with acetone or similar solvent. apply some silicone mould or die release to shaft and assemble the shaft with butterfly plate, into carb body,
If possible get a very thin section "o" ring onto the haft at the inboard section up against the butterfly plate, if not possible twist up a length of teflon tape into a fine string, wrap this around the shaft and stuff it into the hole. push it right down to the butterfly plate on both sides, this will stop the adhesive from getting right through.
Now mix up your Jb weld, bondo or whatever petroleum resistant stuff you can get. Make sure the butterfly is fully closed this will help to align the shaft in the correct position, Press the mix into the gap between shaft and hole in housing, clean off outside and let cure.
remove teflon tape from inner ends of shaft you may find an "o"ring pick useful here, Then you should be good to go. If this operation is well done the results are quite good. Not as good as a new one but a heck of a lot better than a worn one, and no special skill or tools required.
The only problem that can occur is if you haven't applied the silicone die release properly to the shaft. an alternative is to use a teflon spray that dries and then a thin smear of grease.