Everything you've described makes it sound like you're flooding it (emphasis on you). I would venture a guess that not using the de-comp means you are not giving the saw an honest pull. The decomp definitely helps start a 261. You'll realize that the first time you start it with the piston in a certain place and you nearly tear your wrist off or break the cord. So just use the decomp like you're supposed to. Geez -- dock yourself 10 points for not following user manual instructions and then complaining!
For a cold start, with decomp in, it should take no more than 2-3 pulls on choke before the 261 kicks over, at which point you move the lever to fast idle and it should start in 1 more pull. I sure wouldn't pull more than 3-4 times with the choke on unless it was a new saw, or a saw run dry, and you had to move some fuel into the carb.
Note, DO NOT choke a Stihl that has been started within the last 30 minutes or so -- you can start that at idle or fast idle. You'll flood it for sure if you choke it. You may need some experience cutting with the saw to know when it's warm, lukewarm, or cold.
I have zero problems starting my 261, but one of my buddies was using it a few weeks ago and he was completely incompetant at starting the saw. He was flooding it left and right. He really had no concept of warm/cold, when choke was needed, how the lever worked, etc, and he kept trying to choke it. He also wasn't familair with a decomp and wasn't using it unless I reminded him. So I have firsthand experience seeing operator error in action.
If all else fails, bring it to the dealer and they will determine if there is a real problem with the saw before you drive yourself insane. No sense beating yourself over the head with the saw if there's a chance it has a defect or problem.