If you have trouble starting an 0-320 D3G in a Warrior it's broken or you're doing something very wrong.
Do not pump the throttle, this only results in an nice bonfire under the engine.
Definitely do not prime with the throttle. As stated above this just puts a trail of fuel dripping out the bottom of the engine ready to light off with the slightest back fire.
The correct amount of prime is basically all that is needed for the conditions.
I know this because I've had to clean up the mess numerous times after Cessna pilots, including instructors jump across to PA28s and try to start them with throttle pumping. My theory is the Cessna 150/152, 172 have a higher speed starter than the PA28 which allows the fuel to be sucked through. The PA28s much slower starter I reckon inhibits much fuel being drawn through until it fires and speeds the process up, so throttle pumping just puts a pool of fuel dripping out the bottom.
If you be pumping that acc pump as described you are back at flooded engine, surely?
Depending on the engine the fuel may not even make it into the engine to flood it, the flooding may occur in an even more undesirable location.