A nose high trailer will ever so slightly increase sway. The reason is because it will transfer a "slight" amount of weight to the rear of the trailer.
I have race car scales so I know "exactly" what the weights are doing. A few inches up will only transfer a few pounds. Anybody that says that a few inches nose up will cause extreme problems with sway does not know what they are talking about.
I can tell by your post that you have a severe light tongue problem. I have seen some trailers built really poorly when it comes to tongue weight. The only way to fix it is to pack accordingly. The heaviest things up front and the lightest things in the back. Bike rack up front or even a gen set mount on the tongue of the trailer. To fix your problem you have to get the tongue weight up.