@Emil Apologies for disappearing for a bit. I was clicking the red trash-can icon as you suggested, however this didn't appear to change firmware upgrade behavior.
Since it seems like whatever issue is occurring might be device-specific, I'll move this to a support ticket to reduce spam for others following this thread.
edit: Factory-resetting the Hub seems to have fixed it? I had some trouble getting the factory-default password to apply when connecting from a new phone - a couple of resets were needed, but deleting the hub from DM after resetting and immediately triggering a firmware update seems to have gotten my Hub onto 4.4.6.