"My question or concern is that while doing my burnout, the burnout slightly favors the driver side (the side with the clutch packs) now. Launches are straight and hard."
Do you mean the left side smokes more than the right? If so you need to shim/adjust the driver side front spring to get to car level to have the same weight on both rear tires.
My son and I drag race 64/65 Falcons. Both with ladder bar rear and stock type front suspension. When son get in the left front dips so I shim the left front with a spring spacer or part of one depending on amount of levelness of car before starting. Some springs require different shim thickness. We have been racing these for several years.
This would be called 'Ballasted Alignment' and I have been doing this since going to ladder bars.