Great idea!! This happened to me on the very first Blaster I owned, now that you mention it. The RH main (PTO side, as we lawnmower guys call it) seal was destroyed.
What's happening is that the engine still starts and runs on just the fuel from the tank, but due to the bad crank seal, it also sucks the lubricating oil out of the gearbox. This oil is burned, along with the properly-metered fuel/oil/air mixture coming from the carburetor.
The engine will start right up, but it will run sluggishly and start to smoke almost as soon as it fires. And I don't mean the 'worn-out-piston-rings-in-a-four-stroke' kind of smoke. I'm talking a cloud big enough to eradicate every mosquito in a square mile of your house. B)
Yeah. You'll need to drain the oil out of the gearbox, remove the crankcase cover, and take a good look at the crankshaft seal inside. I'll bet a dozen donuts that the seal is damaged, destroyed, or out-of-place. This is an easy fix if you've done this type of repair before. If not, just get ahold of a Clymer or Hanes manual for the Blaster, get familiar with your quad, and take the afternoon off. The job won't take more than 2 hours, even for a first-timer.
Just a note: Your FMF chimney is probably NOT the result of a fault in the oil injection system. The oil pump puts out only enough oil to maintain a 20:1 mix ratio at all engine speeds. Even if you put 10:1 pre-mix (about as rich as you can go and not clog a jet) in the tank AND ran the quad with oil injection, you still would not get this choking cloud

of hydrocarbons.