I have a klv1000 - 05 reg ; had it for 3 years and has 31k miles on it

Never had a problem until 3 months ago when the bike started to struggle to get from 3 to 4 k revs under gentle throttle - the bike seems reluctant to go ; stutters; a tiny misfire or 2 or 3 ; as soon as gets to 4k shes away and goes as well as ever

Has never had this problem before - just happened

I had aftermarket cans on it so changed them to originals which made it a bit better but not right.

I have had dealers do a dyno, check the valve clearances and do a throttle body sync - ITS STILL DOING IT !!! aaaarrggghhh!

Its only slight and doesnt do the big backfire job but its really annoying

Does any one have any ideas that I can try now that the obvious things have been done ; the dealers have got all my money !!

Any help or ideas gratefully received

I own the same year & model machine. I bought mine used with about 12K miles on it. My "stumbling" in that rpm range was worse on hot days, less on cool. This problem is particularly irritating on the east coast because it happens right in the middle of the rpm range where traffic will allow cruising on parkways.
I sync'd the throttles and it didn't help much. The last owner made quite a few mods to the bike and one of them was to remove the secondary throttle plates. He must have had the same problem because he changed the sprockets so the bike cruised in the 4-5K rpm range. That made the speedo terribly incorrect and the rear wheel wanted to lock up on downshifts. Happily, the last owner included all the o.e. parts with the bike that he'd removed. I replaced the secondaries and the problem occurs much less than it did. Now that the throttles are back to the way they were designed, I'm going to try syncing again. If that doesn't remove the problem, I suspect that the computer may be getting signals from one of the sensors that are out of spec.
If you solve the problem before me, please post.

I would check throttle body sync and all vacuum lines. Sounds lean. Might help to try running a little Lucas injector cleaner.