[Bobcat]

If it were mine , I would replace both needle valves and also check the floats to make sure that don`t have a leak/pinhole in them . The fuel today deteriorates fairly quickly and forms varnish if left sitting for any period of time . I had the front carb on my 427 Galaxie do just that last week . Took the float needle valve out and let it soak in lacquer thinner for several hours , checked it for free action and reinstalled ( they were new as of this spring ). Engine ran fine . Same symptoms you had ... the car started fine , started running rough , cleared up some and then wouldn`t start and plugs showed wet .
I don`t drive the Galaxie that much anymore and the fuel sits in the carb and causes problems over time .
Jegs and Summitt both have aftermarket float needle valves from folks like Barry Grant etc that are good quality ... try not to use something from one of the discount autoparts houses as their quality can be suspect .
I couldn`t tell from your postings if the carbs were Holly or not , but if you had a backfire , you might want to replace the power valves ... if leaking , they can give you a fit . Adjust the float levels with the engine running or you will get a false reading .

Good luck.