I'm glad it wasn't just me that had this problem. I have had at least two A-series powered cars that would do just that. Run fine but stumble and die when braking to come to a stop. One was a 1200 with no brake booster, the other a B-210 with a brake booster. Kooky!
The "adjustment" I always made was to "adjust" the position of the stock carb to a new location. (Ususally to the large cylindrical object in the corner of the shop.) Weber carbs have fixed the problem every time for me.