I had trouble with my Anderson until I welded some brackets in place on the frame. If the stock brackets shift forward (and the manual says this is ok) I found that the two brackets were not the same distance from the ball which would cause the bushings under load to pull the trailer more to one side than the other.
I agree that the tires may be causing an issue also and recommend to air them up to max sidewall psi and see how that feels before running out and buying new tires.
As for your suspension, I was also suffering from a squishy 1/2 ton suspension. I purchased sumo springs to assist and it helped greatly with my rear end sag and much better ride quality.
Give it a try- took me a little while to get set but very happy now
2014 Stealth Evo 2850- "Woodstock"
2011 Toyota Tundra Rock Crawler TRD 5.7- "Clifford"
2013 Honda Accord Coupe V6 w/Track Pack- "Julia"
Just glad to get away