Not sure what you’re typing the MAC address into. The easiest way to set up your Sonos with a new SSID is to wire it directly tip-off your router with an Ethernet cable, then go in to the Sonos controller and enter in the wifi data. Once that’s done, you can remove the Ethernet cable.

The nuclear option, of course, is to erase everything stored on the speaker by performing a factory reset On it, then teaching it your new network info using the setup process using BLE, but you’d also lose any playlists you may have set up. 

Sorry, I should’ve been more clear. My apartment complex has their own wifi and I have to register a device by logging into their internet service, and the way to do that is by typing in the MAC address.

Any self-respecting shared WiFi would apply wireless client isolation, for privacy. This will stop a Sonos controller from accessing your speaker. (And if there wasn’t isolation then anyone could control your Sonos, usually in the middle of the night…)

Get a travel router -- or any router with a WiFi-as-WAN interface -- and connect that to the complex WiFi. This will set up a private WiFi which you can use for Sonos.  

Sonos devices have two MAC addresses, one for wired, one for wireless. Make sure you add both. I believe one is +1 the other one.