Great, I have done that same rear swap with my C1500. As I learned, with the heavier diff the current springs are stressed a little more because of the added torque. I have noticed walking of the truck and does not have a specific direction it prefers. Also encountered Axle wrap as well. Are you planning on towing more than the rating of the truck or adding more HP? I am assuming your Z71 is 4x4, with that have you considered what size diff you have in the front. With the rear now a 14 bolt SF 9.5 with the likelihood of 3.73:1 gearing, that would mean your front diff is no longer matched. It may still be a 8.5 ring. that's not a big issue but you have to make sure what gearing you have. Now back to suspension. Have you replaced the leaf bushing in the springs while you are under there? Your differential maybe walking as it is pulling. Mine did when both my truck and trailer was 13980# w/o driver and passenger. I had to stay at 75 Mph on that long stretch of I-20 from Pecos to Big spring. It also didn't help that there was a small cross wind hitting the enclosed car hauler. The helper spring is only there to level the truck with the weight at which the truck is rated. With that being said, it is also illegal to go over the trucks weight rating. Insurance WILL deny your claim if your involved in a accident. Take that info as a disclaimer meaning I will not be responsible if you do choose to overload. When I did my trailer the trailer had little over 7940# on the trailer, 3500# on the drive axle and 2540# on the steer axle. Yes I had it weighed to maximize my tow and hauling. the trailer carrying one ton more then the truck. With both trailer axles with brakes, that made it safer. Also with the upgrade of the rear diff you also have bigger brakes. More stopping power. Unfortunelly, the front disc demotions, pads, caliper, spindle/bearing pack, and bearings are shared between the C/K1500 and the C/K2500LD.
The Bottom Line:
You have four options if you plan on continuing towing you can: Replace your bushings = standard, Replace your bushings and add a swaybar. = good, You can Add a leaf or find a donor 2500LD and take its leaf springs. Then add the swaybar. = Better. You can purchase a Autoflex suspension system. = Best.
Adding a leaf or swapping for the 2500LD springs will stiffen the ride and also reduce axle wrap (Axle wrap is when you put extreme torque or you potentially drag race which can cause your springs to form a "S" shape as the axle rotates the pinion up and into an extreme pinion and drive shaft angle. You can use an airlift air system you can level your truck and keep your easy ride. The autoflex prevents all of this and creates a more stable truck while cornering, even with a load in the truck or towing a trailer. If you are nice to the truck you can use the airlift and a swaybar to help you and be fine. I'm not so nice since I am looking at 600HP area and towing with this truck. Also I like to take it to car and truck shows and its a good cool factor.
Let me know if you have any questions or need more info in the direction you want to go.
