I do the same thing sometimes. When I start dreading being at the gym, I hope on the elliptical and pretend I'm dancing my music. I have gotten some weird looks, but who cares? It makes working out fun.
I also sometimes mouth the words...I also have realized people want you to not work out by them if there are other machines available. I just don't care. These people need their own home gym if they are going to have their own imaginary rules about the gym!!
I think your workout sounds awesome, and you should have walked out there dancing LOL. That would have been funny. But you are not alone in observing these things, or deciding to ignore them!