You should be able to find a spring setup that works for track and street. I am currently putting a pair of BC's on for daily/track use. I am going with a 10K/12K setup which is similar to OEM setup. You could probably do the same but depending on your corner weights might have to up the front(sure your front is heavier than mine).
Are you doing true types in the rear or OEM?
The diff is a no brainer. Switch to solid diff bushings and just throw any of the reputable diffs in there-Quaife, Geiken, Cusco. I bet that alone takes off .5 second.
For front wheels , I would just get an el cheapo pair of 18"x8" wheelsand throw some 100 dollar Goodyear touring/eco low rolling resistance tires on there. They don't have to be top fuel eliminator bicycle tires, but there's no reason to be running grippy 275's up front if you are going in a straight line.
Using spare tires rated to 55MPH sounds a little sketchy
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Also running 4.08 gears at 600 HP would just make your problem worse. The problem is traction, not HP. There's literally nothing else to the equation.