For better weight distribution, I want to race on the track and drag strip. Plus just to be different
I can understand the "to be different" factor. Lots of time and money more than what the car is worth, yes it COULD be done.
For weight distribution??? Really, a 84 is 50/50. Most C4's hover around 50/50, look at the specs. available on this site. My 93 LT1 is just a bit nose heavy at 51/49. Even the mighty ZR-1 is about 52/48 if I recall right.
Look at a C4, you'll notice that the engine is behind the front axle, most of the cars mass is located within the wheel base. The only major things outside of it are the radiator and the fuel tank. The fuel tank does help offset the Front Midship engine mounting location. The transmission is effectively in the middle of the car.
A C4, even in stock form is a capable track/drag strip weapon if driven right. Your 84 especially if it has the Z51 package is a very good handling car even by today's standards. The L83 Crossfire is not going to win many "run what you brung" drag races, but it might make an interesting bracket car!! Then again its a SBC the sky is the limit if you go with other induction setups.
The C5 uses the rear mounted transaxle for many reasons with a longer wheelbase if the trans. was up front it would more nose heavy than a C4, in the back its 50/50, opens up for space for the passengers, cargo, structural rigidity, etc...