welcome to the forum. i have an 08 650 that did the exact same thing from the day i bought it. it drove me crazy. some guys on here told me to buy two #4 washers and shim the needles in the carbs. i did it and it worked. it completely took the low speed miss out of it and it actually ran better. doing this richens it up a little bit. the spitting and sputtering is because it is running lean that explains why it quits when you give it more gas. u can pick these washers up at your local hardware store. brass of stainless steal is doesnt matter. it is a fairly easy job to perform. hope it helps.
brian
brian