Hello,
Do you have a regular or EL? The longer wheelbase on the EL will help some in the stability department.
I have a 34 ft trailer that is a bit heavier than what you are pulling and I can relate to what you are going through. The best investment I made was switching the tires from P's to 10 ply LT's. The P tires were just to soft on the sidewall and the trailer would really steer the truck. The LT tires took most of that away.
Next issue is the WD hitch, I found that a lot of trailer dealers have no clue as to how to set them up properly. My dealer argued with me tons that they were right, my truck was pointing to the sky, trailer was nose high, steering was light and it was dangerous to drive. I had a Reese on at that time and spent a few hours with Reese to get it all setup correctly and all was good. I also had an added anti-sway (friction style bar) installed to further help keep things under control. Not sure what WD hitch you have, but you will need to measure the height of the front wheel-well without the trailer, with the trailer connected, but not using any of the WD features and then adjust your WD hitch, to adjust the front end to get close to the original height. There is a bit more to it than this, but that gives you the basics. Properly setup, your trailer should be level and the truck should look pretty level as well.
You also need to ensure you have enough weight on the tongue, should be between 10 - 15% of the loaded trailer weight.
I have used lots of different WD hitches over the years, and the next best investment I made was going with a ProPride (similar to a Hensley). They are not cheap, hold their value well if you want to resell it and I cannot say enough as to how this hitch has eliminated all sway. Sidewinds hardly effect the truck/trailer now and they feel like a single unit now, whereas with the Reese and others, the truck felt independent of the trailer.
Good luck and hope this helps some!
Chuck