1. Inoperative vacuum-actuated petcock. Check vacuum hose between petcock and vacuum port on carb. If o.k., then . . . remove fuel line from petcock. With petcock in the ON or RESERVE position, crank engine to develop vacuum. Observe fuel flow (if any) from tank (use catch vessel of some sort). With fuel flow when cranking engine, petcock operation confirmed.
2. Moisture contamination of fuel. Although the stabilizer may have prevented fuel gumming, daily atmospherics can deposit moisture in fuel tank. Most effective way to eliminate fuel contamination as a cause, DISCONNEDT carb fuel line, DRAIN float bowl (3 mm hex float bowl drain screw). Insert funnel into fuel line, fill with fresh, "dry" gasoline. Crank engine. If engine starts and runs on known good fuel supply, DRAIN fuel tank (through RESERVE petcock lever position, insuring lower reaches are purged). Fill tank with fresh gasoline; wouldn't hurt to add fuel line anti-freeze ("HEET" is a popular brand name for such an additive) to neutralize any residual moisture in tank.
3. You say carb's o.k., so . . . I can hold my third thought--STUCK float valve; no need to tell you to bash carb to set it free. Similarly, the float height must be correct, the starting enricher operational, given your inspection of the carb. Yet, although your visual inspection indicated nothing amiss, and although you used fuel stabilizer, unseen passages and/or jets may be clogged by crud (ethanol-laced fuel is DEADLY in this context). You may need to soak the carb in an effective carb cleaner to clean these orifices.
You asked for thoughts; those are mine for the moment; good luck!