I have a similar setup, only mine is an SBR. That opens up a whole 'nother can 'o worms when it comes to traveling. Thus, mine, suppressor and SBR, remain at home in the safe when I travel.
It's too bad it seems to be this way. I have a similar setup on an SBR and if I'm traveling in Wyoming or Montana, which is mostly where I travel, and if I want to carry it (loaded, of course), I carry it. It's legal and the police are not a problem. Half of them probably have a setup just like it. I know we're an outlier but it sure is nice not to have to put up with that kind of ridiculous hassle.