carburator problems, '37 Terraplane

I am trying to get my '37 Terraplane driveable and roadworthy. It has a later manifold and carburator on it, possibly '41-'47. It has an automatic choke with a universal choke stove. The heat riser is all rusty and not working. When I start the engine with the choke closed, it runs rich. As the engine warms up it smooths out a little. The choke remains almost closed, like less than a 16th of an inch open When I open the choke, the engine stalls, if I close the choke it stays running, though a liitle rough. I had this carburator rebuilt five years ago, but then I had to change the clutch etc. That took a couple years as I had very little time to work on the car. I did start the engine from time to time. I feel that I am going to have to rebuild the carburator again. Is it possible that a sticking float could cause the engine to stall when the choke is opened. Thanks for all the help. Arnie in Nevada.