C/K 2500 came with 4.3/4.10? What years were these optioned? I thought C/K 1500s only came with up 3.73? Maybe the GMT-400 SS came with 4.10?
OP, I thought the 383 with 4.56 would have plenty of power. At the end of the day, 7,000 lbs is not a ginormous load. You've already spent a lot of money on upgrades. I would not do a supercharger because you are running a 4L60e. Even though it's rebuilt, they are not known for taking a lot of power, unfortunately.
Maybe a 7.4/4L80e would have enough power for you? Are the 8.1/Allison GMT-900 trucks available in your area? The 2500/3500 trucks are heavier and could pull a heavier load, just don't think they will be much faster, unless towing to the max. Maybe I'm wrong?