If you are burning the oil, which I'm convinced you are, here's what I'd do: Drain the oil, leave the filter in, fill it with 5 weight NON-synthetic, then ride it like you stole it, always accelerating, decelerating, for 100km. Then top off the oil, taking note of the amount it took. Do this four or five times, seeing if it takes less oil each time, as those rings seat. If oil use is dropping off, I'd continue until 1000km, or until oil consumption stops, then switch to a new filter, fill it with 5w-40 non-synthetic for a few thousand km, then after you are not burning above normal amount of oil, use synthetic.
If you are still burning copious oil after 500-600 km you have something else wrong: scored cylinder, broken ring, etc. and you will have to start over.
Report back, please. Share what you have done...and learned.