i had the same issues with a BRP cdi, with stock carb. I got a dynatek, and it fires right up.. also runing an HSR Mikuni carb, with electic fuel pump now, and don't even need the choke. it fires on the 1st revolution almost every time.. when i was in barstow at 35 degrees in the moring.. i couldn't get the damn thing to start for the life of me (with BRP cdi). I have also heard from a slew of other people they have hard start issues with that thing.
but they are a thing of the past with a dynatek cdi..plus the electric fuel pump makes sure there is fuel ready to be sucked in when you crank it. the stock fuel pump is based on vacuum, so it only starts working once the engine starts cranking. If it has been sitting a while,, chances are, the fuel has drained back into the tank, while you are doing all that cranking, the carb isn't seeing much fuel until it gets pumped all the way in.. stock fuel filters don't flow worth a crap either. Rhinocrap told me to do the "blow" test.. and its very restrictive compared to a regular aftermarket unit.
so ditch the BRP cdi, and put in a new fuel filter... and you should be fine.