340 not running anymore...Help Please?

At the very least you could pick up a cheapo choke kit at the local parts store and install thet. Then you'd solve two potential issues. You would have choke control which really helps our old MOPARS, and then you also cancel out the chance of the choke beig sucked closed. Im wondering if thats not whats happening along with the fact that it sounds like the carb needed rebuilt anyway.
I have my Eddy carb that I went through something similar with recently. I actually adjusted the Secondaries to kick in a tad later than it was when I started. I have been driving it on the Interstate a lot and it has helped to not use as much fuel, cause the secondaries arent so far open, or may very well not be used while Im cruising at 65MPH.
Def. sounds as if you have fuel issues though.