Gear ratio help

I need help figuring out what gear ratio I need to run.

1.) It's street and strip all wheel drive.
2.) Tire size 295/65-15 slick all the way around. Same OD in a street tire.
3.) Engine makes 600ftlbs from 3,700 up and 600hp through out, naturally aspirated.
4.) No prep racing.
5.) Nitrous is expected 100-300

I was going to try to use the factory gear's but with so much wear in the gear lash that I doubt it would hold a half throttle launch without stripping teeth off. (we are talking about a 1/4 rotation in the pinion.)

I don't have tires yet, should I go larger?

I'm going to talk this out and see if anyone cares to add to my ramble.

Racing at no prep events I would suspect a bias ply drag slick to be the best option for traction.
A tire with tall sidewall would be nice but it would just add to the lack of steering under power.
I could run a short tire with a short sidewall and in theory it will help with steering. I could just tune with gear ratio's. (collect a couple off Dana 44 IFS center sections and 9" center sections.
Would running a 17" wheel allow to run a taller tire with a short sidewall.

If you slicks I would go with the stiff sidewalls