I went through the same thing. There's a few things that holding the 1500 back from being a solid work horse. If you don't get the factory 4 corner air suspension, the coil spring will leave you sagging with a decent load. No biggie, I ordered air bags to correct that. With the bags and WDH, the sag was gone but then I started getting the squishy feeling you're talking about with heavy loads. As other mentioned it, it's the stock tires... and probably the fact that I was right at my payload limit. Then it all hit me, the truck was designed to handle well, comfort, and light duty and I was slowly degrading those features trying to make it rugged enough for some medium to heavy duty. My solution, I traded it in for something that would be more than capable and let someone else enjoy the 1500 the way it was designed to be enjoyed.
1500 payload
100# nerf bars
75# tonneau cover
50# Air bags
800# tongue weight
235# driver
150# passenger
Was at 1,410# without tools, luggage, and additional passengers before hitting the road. Yeah, the HEMI is capable to pull everything I have and I stayed within my axle limits, but the tires and suspension (and payload) were the limiting factors.