A better shock will definitely help with some of the porpoising you are talking about. I have installed Bilstein 5100 series as it was highly recommended by many I asked and once I installed them I agree with them! They are a little on the firm side for daily driving but REALLY help when towing!
A WDH with sway control on a 30'+ trailer is a MUST!!! Definitely find one that is slightly over rated for what you will be at but not too far as that will create a harsh ride! Being 30' long I suggest trying to get more like 12-15% tongue weight rather than the minimum 10% that is generally stated. I actually am in the process of having my work (sheet metal facility) torch me a custom 1/2" thick steel plate to cover the A frame of the tongue of my trailer to add additional weight to help keep the trailer under control! I have experienced some squirmy trailer issues as well like you mentioned behind both of the trucks I mentioned and have come to the conclusion that I am too light on the tongue for the overall length.
You are on the right track with some E rated tires. As well as if you are still having some sway issues I may suggest a stiffer rear sway bar for your truck! Hellwig 7709 Rear Sway Bar Dodge Ram 1500
You probably wont notice a LOT Of gain from this as you currently have a sway bar anyways but this would help stiffen the stock bar up some...
Something I may suggest to see if it helps the trailer behave a little more for you is to try and add some dead weight to the tongue of the trailer. I added a tool box for my battery and placed some dry concrete bags in it to add dead weight and see if it helped or not. In my case it did.... I also re located the spare tire from the rear of the trailer to under the front tongue in an effort to get more tongue weight!
Are you getting the hint that I needed more tongue weight?