Francis K. Lalumiere
I heard here on BGG that at one point there was a mechanism for changing the move order during the course of the game. This was dumped from the design very late, after the board and pieces had already been settled, so the whole "move columns around" thing is now pointless. Moves happen in clockwise order.
When we play we ignore that part of the board and only use the columns to put underneath the disc you decide to build on your turn, just like you suggest.
Edit: And in case you are new to the game and haven't heard - please try playing without the bonus cards that are awarded for finishing a monument. The game plays much better with no bonus for completing a monument at all. Just leave the cards out of the game and play everything else as the rules suggest. The cards were an addition made by the publisher, and they tend to unbalance the game and change the strategy for the worse.
Thanks, W M.
Yes, I'd read about the special cards, and we don't use them anymore (I hated them, so no hard feelings there...)
But I hadn't heard the story of the turn order manipulation, so I kept thinking I must be reading something wrong about those little columns. Glad to know we've been playing it right all along!