The oil debate is always long winded. Fact is, unless we're talking the newer energy conserving type oils (which I'd never put in a motorcycle), any oil is just fine as long as it's the proper weight/multi-multigrade IMHO.
By its nature, synthetic oil is almost all additives. But a quality syth oil will outperform any dino oil. That's why they recommend you do not put synth in a new engine as it just wont break-in very well.
Motorcycle oils VS. car oils...it's marketing guys/gals...a way to get we the enthusiasts to spend a few bucks more. There are no official studies that show they (motorcycle oils) are superior. If you know of one, please share. Information is power.
As to why that engine is smoking on start-up...could be a few things...
Your running that home-done-filter on the side of the bike. If it wasn't oiled (K&N), or the seal it has to the airbox is not completely closed, you could have pulled some grit into the motor that's damaged the rings or cylinders. Then you would have a smoker on your hands. I doubt that is your trouble though.
Leaking value guides...might be.
Could even be a fuel issue as you suspect. But if it's blue smoke, I've always been told that was oil.
If your running a much much thinner oil than recommended, then it could be sneaking past the seals as the bike sits and burning off when you start it up. Some older bikes had/have this trouble.
As with all things like this, my advice is, if you suspect something is wrong, take it to the dealer and have them check it out, or at least document it, so if you end up with a major repair it should be covered.
Your bike should not smoke though. Get a leak-down test and a compression test done.
Last thought, just like running an engine too lean is bad, running it too rich can bring it's share of troubles. The excess fuel scrubs the oil film off of the cylinder and lead to premature wear.