Taken all the steps to prevent sway. Still swaying. Help!

I think your problem is simply that you don't have most of your weight over the wheels.
You said that you have most of it toward the front. That is a mistake

Your trailer should be on the same plane as your TV.
Stand opposite and look and see if they are both parallel to each other. If your trailer nose is down or up, it will sway all over the place

Guy