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

Check all your weights.... there are lots of posts here on how to do that. You could be tongue-light, regardless of how you load the trailer.

My next thought is that there is a problem with axle or wheel alignment.

With that size trailer make sure you have the right size bar, and use 2 of them. You might consider upgrading to something like an Equalizer or Blue Ox Sway Pro hitch.