Nothing to lose by checking the advancer but I think full advance is at about 3500 rpm so by the time your issue occurs at 4,000 rpm the advancer has done it job ? You can check that it is not seized and if necessary invest in a timing light and test as per the manual
If your issue occurred at 3,000 rpm then I would suggest looking at the pilot bypass circuit in your Keihin carbs but then I'm not familiar with the 440. Still , if you have the carbs off again then perhaps worth a look ?
A group of 3 tiny holes just behind the throttle butterfly. Very easy to miss when carb cleaning. A small fine pin with the tip bent at 90 degrees will work - be gentle.
Hardrockminer makes an excellent suggestion to check fuel paths for >4,000 rpm which I think in your case would be the primary and secondary jets. Your 440 manual has an excellent section on the carbs starting on page 148
Also take the bowl off and remove the pilot plug and wearing eye protection - very important - block #6 with a finger,spray carb cleaner in #4 and watch (eye protect) for it to exit at #3.
One last thing.
You say the carbs were cleaned but were the float bowl fuel levels set using the clear tube method ? If not then this wont be the cause of the issue at 4,000 rpm but an imbalance might cause "takes off but sounds like crap over 4,000"