Sounds a lot like what I had when I'd had the bike for a similar mileage. I was concerned that my Tenere might have FI issues (this is my first bike mind).

Anyway, turns out it was just my chain getting too loose! The manual specs have the chain a lot looser than on other bikes (confirmed by my mechanic) and after having it serviced by my dealer the setting they used was just loose enough to give this effect after my 6000 service. I tightened it myself afterwards by a small amount (once accessable twist on the adjusting nut with a spanner) and it was enough to get rid of this effect. Needless to say overtightening a chain is worse than having it too loose so don't try that either
The chain should just be able to touch the swingarm if you push it up (without having to press too firmly) based on my dealers adjustments and my modification to clear the jerkiness.

It is particuarly noticable on a low constant throttle (30 mph in 3rd particuarly) which seems to be what you've had, and results in the bike jerking around a lot and a delay in takeup of speen when you open the throttle.

Of course if I am teaching you to suck eggs then feel to throw them back at me