Maybe the best thing to do would be to get one of the suspension guys at a track day to set it up and advise on tyre pressures too as that's where you're finding the issues.
'100% suspension' made a good difference to mine and 'Parkitt' have a good reputation too. Are you close to MCT in Stowmarket as they also have a very good reputation?
Then, if possible, have somebody follow you round and watch what your doing, an instructor at a track day should be up to doing this.
Maybe I'm just getting less fussy in my old age but as a bike to be ridden on track with, at the moment, fairly minimal mods (but suspension set up by 100% at Cadwell as it was a bit 'wallowy' at a few places) I can hardly think of a single fault with it (at my level). I think, as a road bike - mine is a 2013 bike - with just track tyres it's unbelievably good.
I find it changes direction so easily and mine holds a line without me having to think about it. It's that much quicker at dropping into turns than my previous bike that, at corners I know, I seem to be caught out by it's speed of turn-in and I'm quite often aiming for inside the curb at the apex.
I'm not sure what to say about the brakes! It's by far the best standard braking set up I've ever used. Maybe try changing fluid but first clean pads and discs thoroughly and see how that works out.