Well in my defense, I actually did try that before asking - not quite that much but I did drain the bowls and let the carbs dribble before giving up.
It did stop after a while, then started back up, then it stopped, then 2 of them dribbled, then all 4, random so far as I could tell. Very obviously a sticky valve.
I'll just keep at it I suppose - might just take a bit more than I was tolerating.