I also asked Arctic Shorex about this. Here's the personal response (not automatic) I got from their General Manager.
"This will not be a problem! The buses are very close by at the port so you should be quite fast to find them! We usually always schedule departure 30 min after the docking time of the ship and it runs smoothly! The guide will be waiting at the port with an Arctic Shorex sign! "
So I'm going to trust them and not worry about it! We'll just be diligent about getting off the ship as soon as possible after docking. The tour sounds amazing, and we're looking forward to it.