If you have a 10K gvwr truck and your scale weight is 8360, doesn't that make your payload 1640? That for all weight - passenger, luggage, stuff in the bed but since it's a scale weight probably includes the driver, fuel, hitch, etc. It's worth remembering that it's pretty possible to spec out a F250 with pretty low payload if you try. All you need to do is add the full size cab, a long bed, the diesel engine, the 4WD, and you have a low payload truck.
A couple of other thoughts. The payload is a theoretical weight distributed ideally across both the front and rear suspension. Your 16 bags of cement were probably all behind the rear axle., at least that's where I would put them. In other words a worst case scenario for load distribution. The rear springs are variable rate, as they get loaded and engage the overload spring they get far stiffer. That means that if you needed 1,000 lbs behind the rear axle (or directly over it) to get to 1/2" from the bump rubber you might need another 500 lbs to get the rest of the way. As noted that's how they got the super smooth ride unloaded.
2005 F250 XLT Supercab 4WD Shortbox, stock as possible, "Blue Spring", Scangauge II, Autometer fuel pressure and voltmeter, Bilstein HD shocks and steering damper. Rotomaster turbo