Based on David K's request, I created a PDF for print and play turn order placards. I uploaded them to the files section of the Sunrise City page. It may take BGG a few days to approve the file, so keep an eye out for it.
Just cut and fold the placards into A-Frame standees and then distribute them each round after role cards are revealed. It may help to lessen the awkwardness of non-sequential play.
Most of the games that I've played with variable turn order instead put player markers along a turn track. That way you can look in one place to figure out how many steps away your turn is, and which order people will play in, rather than trying to hunt around the table.