Looking for Carter BBS single barrel, w/U-shaped linkage for throttle arm (not cable type) 1963.

I pretty sure there is no such animal. The BBD is a 2 bbl carb. A 2 bbl carb was not available on the slant six until after 1966. 1966 was the last year the "twisty" linkage was used. There might have been a non USA application of the BBD with that linkage, but I don't know. You can remove that bracket from the single barrel carb and attach it to the BBD. I did that with a Holley 4412 500 cfm 2bbl.