Keep in mind that the manufacturers use OCI's to preserve engine life--
but also to attenuate engine life.
In short, they want the engine to last long enough that you say to yourself "This is a good product, I think I'll buy another when this one wears out."
But they don't want the engine to last so long that you don't need a new bike in, say, 50,000 miles.
The motorcycles which have gone the farthest documented miles with no engine problems and no over-hauls did so on 2500 mile OCI's. Those were two Harley Davidson engines which each went over 400,000 miles on 2500 mile OCI's with conventional 20w50 oil. Some BMW engines did similarly. Not sure of the oil type in the Beamers, but they did swap it out every 2000 to 2500 miles.
Get the oil switched out sooner--not later.
Especially in a system where the engine oil lubes the transmission, you want to change the oil at the very least every 2500 miles. Were I you, I'd do it every 2000 miles, and change the filter every 4000 miles.
While the filters can do a good job of keeping the larger particles (10 microns and up in many cases) out of the oil pool, the body of the oil still accumulates the smaller particles over time. These untrapped particles may be too small to create problems (since they are likely smaller than the hydro-dynamic film) but when that film is breached,
there they are. And the very fact that those particles are there--even in the extremely unlikely scenario where the hydro-dynamic film was never breached--means that they are displacing lubricant at the very least. Can that be a good thing? I'll answer that:
No.
Synthetic oil won't help this situation. It'll just cost more and make it less likely that you'll get your oil changed out when you should...
The motor oil has been called the "trash dump" of the entire system, and that's a good analogy.
Use a good diesel engine oil such as Shell's Rotella 15W40 and change the oil every 2000 miles. Such an oil will shear less, and do a better job of protecting your transmission. Sure the factory oil will work to lube the transmission, and I'll bet you can get 50,000 miles or so on that transmission before it goes all screwy on you... (Which is just what Suzuki would like to see).
If you want the bike to last longer than fifty thousand miles, protect it better with short OCI's and it will.
See if NAPA has a filter equivalent for the oil filter. It'll be a Wix made product, and certainly as good or better than the factory offering--at around 1/3 the price.
Dan