I'll conclude this thread by saying that the problem is solved and it was indeed the petcock. Replaced with a new OEM petcock (purchased from Z1) and a new plug. I opted not to rebuild the petcock because it was leaking from the side -- actually blowing fuel bubbles -- and from what I understand, rebuilds are not always successful. New petcock cost about $75. Rebuild kit was $50. Started right up on 4 cylinders.
Bike runs better than ever partially due to a better seal from the new carb intake boots. Not only do they seat better, but I didn't even realize the airbox could be moved forward -- the last owner had it in a mid/back position and the boots were barely hanging on.
I was about to go for a lengthy ride and noticed the sidewall of my front tire is badly cracked. It's not even that old. Just dropped the fron wheel off for a tire change. Can't win this year, I guess.