Nice thread drift. Never had any issues starting a Warrior (O-320) the standard way, from memory it was several primes if cold, mixture full rich, throttle at the 1500 rpm position, crank and when it kicks over retard throttle to idle rpm. A Hughes 300 IO-360 was another beast altogether, open throttle a tiny bit, prime if cold, fuel pump on, mixture full rich for 3 seconds then mixture full cut-off, fuel pump off, crank, when engine fires quickly move the mixture to full rich and set throttle at idle rpm. If you did it right it would start on the first crank, if you did it wrong you'd be cranking for ages with rest gaps in-between screaming "start ya' b@stard'.
Re carburettor icing, I had a situation once when practicing engine failures under instruction. The carby heat was confirmed working during run up and was applied during the engine failure simulation, however the simulation probably went longer than usual as a better field was selected. Upon reaching the safe lower altitude and applying full throttle the engine started shaking the plane quite vigorously with only just a tad over 1000 rpm indicated at full throttle. Still, you could climb a Warrior with that limited power, a little flap and pointing into wind, and we managed to gain enough altitude for a straight in approach (rather glide from the reporting point). The reason for the carby icing was not doing any engine revs during the prolonged simulated engine failure to bring back some heat into the exhaust manifolds that feed the carby heat unit.