I plead guilty to having towed heavy! LOL! I pulled a 16,000# toyhauler with a 2500Ram. I was over gross wts, but within axle limits. I have years and years of truck driving. I went with that.
I bought a bigger trailer, and the rear axle wt went over. I added dually wheels to the pickup, and air bags.
With an empty pin wt of over 3000#, I do not think there is any way you will be within your rear axle wt rating when trailer is loaded, and you add the wt of people and stuff in the cab.
You should get a dually, or convert yours.