If the tank is at the correct level then fuel shouldn't run back from the carb unless it's a tail dragger that sits very nose high. Priming an engine involves more than just getting fuel up to the carb, a small amount of fuel has to get inside the engine and then get spread around up into the cylinder where the plug can fire it. It's a bit of an art to get it perfect but a little practise will soon have the engine starting on the first flick or bump with a starter. Usually 3 or 4 turns of the prop after fuel has reached the carb (at full throttle) is enough to start spreading it around by giving a few quick flips of the prop until the engine begins to sound "wet". You'll know the engine is ready if you connect the glow ignitor, hold the prop firmly and turn the prop slowly over compression. The engine should fire and kick the prop back against your hand.

With any plain bearing engine like the LA you must be sure there's oil around the steel shim thrust washer behind the prop driver when you use an electric starter or you risk damaging the crankcase. With hand starting this doesn't matter.