During the reset procedure for the AX, it comes to a page that asks me how I am connected to the internet. The choices are basically cable, ethernet, dial up, or "I am not connected to the internet right now", which is what I am selecting since none of the others make sense. If I select cable it takes me to a page with a lot of server info to fill in, as I recall.
Basically, the AX is expecting to be connected to an Ethernet-based Broadband modem with an Ethernet cable. There is no option for connecting to a wireless network for Internet connectivity, except for the following two cases: 1) The wireless network is provided by another AirPort and the AX is configured to extend it, and 2) You have a 802.11n AX and have configured it as a wireless Ethernet bridge. In this second configuration, the AX would "join" an existing wireless network (it doesn't, in this case, need to be one provided by another AirPort), and then, feed the Internet connection out its Ethernet port for wired clients.
What we are attempting to do here is NOT use the AX for Internet access, but just for sharing the printer. The AX normally does not have an issue doing so as all that is required is for it to join an existing wireless network as a wireless client ... BUT (again) for some reason, the AX is not joining the Hotspot's wireless network properly.
I assume that this Hotspot is a Wi-Fi network and not a cellular one (CDMA, 3G, etc.) ... correct?