I am really lucky to have discovered the sweet spot for priming my engine and i think this is what you need to do. If there is the right amount of fuel and air and a spark nothing is going to stop it starting. Two or three pulls with no start means one of those three our out of balance.
For me, the procedure is to lean the engine over to the side to prevent flooding the carb. Pump the bulb to get the fuel up to the carb and one extra push to squirt some fuel into the carb (you can hear it go in). Put it ON MY BACK give the cord a gentle pull forward to get it to a comfortable position and ideally move the piston over top dead centre and then a swift smooth pull out to arms length. Usually goes first time even after two weeks of no flying.
Practice that priming and yes, leaning the machine has certainly helped me, I used to flood the engine,
Please dont start the engine on the floor. I know it's easier but only if you are doing it wrong - I confess after I had flooded it I used to put it on the floor, Fully open the throttle to let lots of air in and pull away at the starter until it sparked up. Thankfully I still have two arms!
When you find the sweet spot for your machine it is like a zen experience so keep working at it.