I'll keep this simple. I doubt you will be on the autocross or drag strip every weekend and the car will see more miles on the street, right? Build it to handle well since it will be a nicer car to drive on the street. Having a good autocrossing car will be a by product of that. A car setup just for drag racing won't be fun to do any real street driving with. Don't be afraid to use large t-bars, like something around 1.12, just get some good shocks to control them. Sounds like you have the HP to run a decent number. I'm not sure what "hold it's own means" because that can be a vastly different number based on who you ask. A 700HP engine in drag prepped car should run low 9s easy. I don't see any reason why you couldn't run 10s with it in street trim.

I've run the Grand Champion event at Moparty for the last 2 years. We autocross, drag race, and speed stop. I used to drag race a lot. My car is set up for autocross/street now. While drag racing is fun, the autocross is much more fun and I'd rather have it perform better doing that. Not to mention street driving is a blast. It's fun to cruise down the interstate keeping up with modern cars and taking exits at high speeds.