mbbackus No Problem. But I need some help to understand your plan. Wireless is not my world.
You said in the OP "I only have access to a WiFi network (no ethernet)". So it is a Wi-Fi network, a mesh, not a single wireless access point which connects the Wi-Fi clients to the Internet through an ethernet (cable)?
If there is no ethernet (cable), how does the MoodleBox get an IP address? (MoodleBox assigns 10.0.0.1 to its own wireless interface. The ethernet interface depends on a DHCP server.) Well, unless you set the IP addresses manually on the ethernet side. And then, you need to edit the config.php of Moodle and run ./admin/tool/replace/ to search and replace the FQDNs.
I think, I need a sketch to understand.