I just had the forks re-built when the springs were put in. I've been thinking more and more the rear shock is where most of the problems are coming from. Common sense I suppose, but the further you lean, more worse the shock performs, correct?
I estimate there are about 3000 km of track day mileage on my 919.
(but I haven't tracked since the end of 2011 when we lost our local track)
I only tracked it after doing the suspension.
I have never experienced what you are describing, if anything, the very opposite.
The stock rear suspension piece is not really a damper with spring, instead it's more of a thing to hold some coils of mush.
The late model rear is so undersprung for what you are doing, it's offscale.
The frame is not THE problem nor A problem, at least not for mere mortals on street tires.
Properly done and set up front and rear suspension units transform the bike.
Nicely done, a 919 is a rock steady forgiving platform that much more easily allows newbies to have their brain speed stay get up to the bike's level of brain need.
One thing I did notice though, was that the 919 rear to me felt like it had more tire sidewall wallowing until it heated up, than my 750 GSXR did with the same cold tire pressure setting. I ended up using a wee bit more pressure in the 919 rear as a result.