Just had to deal with a lot of fun with these carbs not that long ago. My biggest gripe with these is the really really really stupid float bowl design making it an easy leak point.
Holding the gas pedal down a bit is actually the suggested warm starting method for these engines. I forget where I found the Mopar brochure that had cartoon depictions showing this. The fact that it wont idle is another matter though. Check for vacuum leaks first then five it a proper deep clean and see if that fixes anything.
If you're really done with the 1920 (as I was before I figured out my problem) talk to slantsixdan about getting a new old stock Carter BBS. I'm not a fan of carbs to begin with so I told my wife that the next time her carb starts acting up I'm converting her car to fuel injection. Its a big job with a good amount of fabrication, but I find that stuff fun and we'll get all of the benefits of EFI.