This is on the gas, coming out of turn one at Manfeild here in New Zealand. I had been running (old) Michelin Pilot Race tires on it for years in 120/60 and 160/60 sizes and the bike's 'stance' on the road had looked fine. I have an RVF400 front end fitted by the way, hence the wider front tire size. I recently changed to some beauuutiful new Michelin Power Ones (soft compound DOT) in 120/70 and 150/60 sizes. These are the ones in the photo. The front tire has a 10mm greater radius than the old one and the rear has a slightly lesser radius, which had the effect of tipping the bike nose high. As you can see in the photo, i ended up with a similar stance to yours.
Luckily i have an Ohlins 46HRCL remote resevoir shock which has adjustment for length/ride height. So i've since wound it out to maximum length to jack the rear end up which has compensated for the difference in tire radius and then some. Andy and others tell me they have had good results with this adjustment too. I also chopped 20mm off the length of my fork springs to lower the front end down to compensate for the taller front tire. You can achieve the same effect by merely dropping your forks through the triple clamps if you like. The RVF fork doesn't allow me to do this.
If you can find and afford one, the Ohlins shock is a nice, trust worthy replacement part but you'd probably get better results for the money by finding a standard NSR shock and having it rebuilt. I paid £400 for my Ohlins five years ago, bought from HPS in Alfreton, UK (near where i used to live).
As for tires, i've been extremely pleased with the Michelin Power Ones but the minimal tread means they'd be useless on a day like your Mallory trackday so i'd only go with them if you want to get a second set of wheels for wet tires (which is what i take with me to trackdays). The Power Ones were really expensive too unfortunately... Both the bridgestone tire models you mention look good and the prices seem good online (i'd seriously considered them myself). I recommend you try 110/70 and 150/60 sizes of which ever tire you go for.
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After years of moaning about immigrants now i am one...