1st question, is your 383 broke, junk or blown up? If yes, then ognore the next sentence - your 383 with boost will meet your HP needs EASILY.
Assuming the 383 is no good, Any LS with a GT45 or VS7875 will get you in the 11's at 12-15psi of boost. I'm cheap, so take all of my next comments with a grain of salt, FORGET FiTech, frget the Diamond forged pistons and rebuild. Is your current transmission a TH350 or TH400? If yes then either will work if built properly. If you want a 4L80, then that's a great option as well. A stock rebuilt 4L80 will handle 1000hp without any special parts.
Regarding engine management, if you go with a 4L80, then a Holley Term X Max is by far the cheapest program available and the bonus is that it comes with brand new harnesses, O2 sensor and can be hooked up and running in about 4 hours if you hurry. If no 4L80, then either a Holley Term X or Megasquirt. 80lb Deka injectors will get you to your goal without issue. Sloppy Stage 2 cam with Pac 1218 springs.
My best advice : don't reinvent the wheel. And a 6.0 is a better plan, but when push comes to shove, a 4.8 with 200K miles on the ticker will get you to your goal.
As Chris mentioned, there a bunch of threads here with turbo LS builds. And I agree with Fleming, HP Tuners is great if you have the time and ability to learn it.
Again, dump the FiTech plan - that system poor and the support sucks.