Yeah, it's definitely not unnoticeable, and I too found 'stiff' suspension to provide a superior driving experience with a yard of clay in the bed...Used our truck to help some friends demo an old pathway. I threw down some old plywood prior to loading as not to totally screw up the bed.
Anyone who says they don't notice that much extra mass in a vehicle isn't paying attention. I will say, it handled it like a champ, the air suspension took an extra moment to come back up from kneel mode to standard, but it leveled out and drove far better than I exoected. I also found sport-stiff-low to be a good stable platform. I didn't try tow mode, not sure why honestly.
As much as I really wanted to do a followup 0-60 test, I couldn't bring myself to going full dumbass with that much weight. I will say, it still had plenty of get up and go, while still providing a very predictable deceleration curve via regen.
What was hilarious was most of my coworkers either drive full or mid sized trucks, and each one gave me the "what the eff are you doing to that truck?!?!" comment, but at the end, came away more impressed it wasn't just a pretend truck.