Did you soak the pilot as well ??? , light thru it is not a 100% indicator it is "clear" , I personally look thru mine with a penlight , and a magnifying glass , that way I can see if anything is even slightly restricting the passage , if you see a light with a cross in it , it is partially clogged , it should be a round light ............. If it was a ignition issue you would most likely have less spark or intermittent spark , so richening should actually make the issue worse , and leaning the mixture should make it better , so maybe try messing with the needle position and see if it improves by lowering the needle which would lean the mixture in the mid range area , or if you have different size jets , try them , if it is leaner and runs better then ignition could be the issue , I would think ..... not saying it is not a ICM issue , but it could be stator as well ........
What is the fuel screw set at ???? , this will give a good indication as to a fuel or ignition issue , as will the plug ... speaking of plug , the spark plug cap may be a issue , there is a resistance test for it , as it has a resistor in it , and they have been known to go bad from time to time , it would be nice to rule that out as a culprit ...... , I have never had a ignition issue with my 06 , and aside from the initial valve issue , which I solved with Stainless Intakes , I have not really had a "mechanical" issue with mine , it can sit for a year and fire right up (I have a mix of Av gas and Non Ethanol Premium in it) and it has never failed to to start and run well , except when the Intakes went bad , I can literally leave it sit for a year , and take it to the MX track or the woods and never have it even so much as sputter , it will fire right up and run like a top ....... but the claim that after soaking the carb , and the issue did not change , has me wondering , if it was fuel related you should have seen a improvement , whether complete or partial improvement , which was not noticed , and that would indicate a electrical issue .....
Just as another item to check , have you checked the stator output ?? , and checked to see if the battery is charging ?? , just because it runs , does not mean the stator is working as it should ....