From a dull memory of bringing old cars back to life a sharp rap with a spanner on the side of the float bowl would often stop the overflow. I also noted over the years that the design of the needle altered to have a rubber tip which i imagine may have been an improvement on sealing. Not sure how well the rubber tip might operate with bio fuels or indeed the floats, given I think I read somewhere that Ferrari may be supplying brass floats for their older cars..
Just as Richard suggests a rebuild kit would seem to be the way to go for carbs that may not have had the benefit of new gaskets, needle valves fitted in years..
http://www.southerncarbs.co.uk/page_1822386.html