I may be missing something about how Robots work, but I can't seem to get my bots to use the tower. It's within their Logistics range, it's connected to their Roboport, yet they ignore it. The bots just pile up at the Roboport and wait in line to be charged, none of them even thinking of using the tower.

As you might know, bots use the nearest port or charger to charge. They normally take into account wait times, but distance is a major factor when calculating for that. I don't know how close your charger is to the robo port, but I suggest having it either in the path of the bots that need charging between where they typically come from and the roboport, or to have it right next to the robo port to increase the chances of them using it.