I feel your pain - the pretreatment they put down is the same calcium chloride used for ballast in tractor tires - it will destroy rims around the valve stem, after it east out said valve stem. Actually had that happen on an old Ford 2N just...
I'm guessing that it may be as simple as needle and seat - the hard warm starts could be from gas dripping out if the carb due to the seat not sealing. Shine a flashlight in the carb and see if it drips while running. If so, then it likely is...
Timing seems to be what it needs to be. Is the fuel pressure staying when shut down for extended times? If it bleeds down, that can maybe be the reason for needing to fire on second attempt.
Not really about distribution, more about keeping it from splashing around and causing drag. That's how a windage tray in the pan works anyway, not sure the purpose in the valley, unless perhaps more about temperature control to keep the intake...