Your bike shouldn't be smoking in 4000 miles... NO WAY! Running the crap out of it
will not solve this particular problem because your rings are already bedded in as good as they are going to get. You could rehone the cylinders and replace the rings and do that....
I don't think so....
You may have to take your bike down to your dealer and get a leak-down test. Your problem is more than likely a bad valve seal. Oil is making its way from the top end of the motor down into the combustion chamber; probably on one or more of your cylinders. Some said to check the plugs? That might be a good idea to see how even the cylinders are burning or if you have an oily plug. That could point you in the direction to find the problem.
If you are running the synthetic oil and have been doing that from the very start, it is possible that your rings did not bed-in properly. However, running the snot out of it with a non-synthetic oil now is not going to help you at this point. The synthetic oil that you are using is
5W40 oil. That particular weight is not recommended for your bike by Suzuki (see chart below and check your manual)
I would dump that stuff and put in a recommended oil grade before taking it to your dealer. This is especially true if you are seeking any kind of warrenty claim. Lots of guys will give you their opinion on a non-recommended grade of oil because they "think" they know more than Suzuki about these bikes. I laugh my ass off everytime I hear that. Some of those guys are seeking maximum hp out of their bikes and might care less about engine longevity or they just want to be diffferent and say its good because my engine didn't blow up or my cams look good...
As a first step, I would put in some heavier weight oil (10W 40 or higher) and see what that does. If you live in a hot climate (like me) go to a 20W50 and see what happens with the smoke. It may stop the leakdown from the seals or stop it from getting past the rings, a little, which would help your smoke situation (at least visually).
I also know that Ivan jet kits can run very rich if not set up properly or you didn't get the air box drilled right. Also, Ivan also released some needles that were not quite right in very early production making the receiving bikes VERY rich. What was the origin of your jet kit? Did ya get it new from Ivan recently or did ya pick up a used kit off of someone? Extremely rich bikes may give the appearence of smoke but I don't think it would be BLUE smoke. That brings us back to an oil related problem.
Good luck.