As mentioned before, a light shot of horsepower on demand (N2O) is, in my opinion, the best way to achieve your goal at the track and still meet the streetability goals you have put out there.
600 streetable, mild mannered HP is pretty easy to build, reliable and not overly expensive. With most fully equipped, ~3,500lbs. all steel cars, this is mid to low 11's.
The NX kit I bought was under $500 for everything and knocks about 1 second and 10mph off with very little effort.
I wanted a NO COMPROMISE street car and, for the most part, that's what I built. The rollcage and spool are exceptions to that.
A true 600 horsepower in a 3500 pound car will be WAY faster than low to mid 11’s.
My 3280 pound 360 doesnt even make 500 and ran 11.20’s in good air when i still had a 727 in it.