I think I need to go to Carter BBD Skool !

And is there a fix for the shaft leaking on this side?

The standard practice is to ream out the base plate and install bronze bushings. There are 2 things against this. Not enough room in the base plate to ream it out, and nobody makes bushings to do so.

And yes, you can make bushings. But at some point, there is diminishing returns on the costs involved. And just how NOS was that carburetor? NOS can mean that the carburetor had bad throttle shafts and was replaced with something better. And somebody just picked it up out of the discard pile and sold it online.

The BBD has always had this problem, that is why it was a great carburetor 50 years ago, not so much now.