There's some details missing that prevents us from offering advice. Are you sure you can't use something at home temporarily? How far away is the car from your unit? If you switched to a powerful mesh wifi, you might consider moving one of the nodes out closer to the car for it to connect, then bring it back in. Or if there's a good place out there, hide it near/plugged in.
Like you already mentioned, it might be a best first idea to knock on some doors (with Liliha Bakery cocopuffs) and explain your situation. Someone just might let you piggyback their signal.
Some of those services where you are saying the Tesla can't connect? You first use your browser to establish the connection and you agree to its terms, then it lets you stay connected.
And not sure if it still the procedure, but if you use your cell phone to connect to your wifi, can't put the car in drive, else it disconnects. Is that what you have been experiencing?
Finally, desperate? Generally your car will auto connect to the Tesla SC wifi (or at least it used to do this), once you have a work ticket in their system. You might be able to drive down/by the SC, sit outside the gate, and open a ticket. It might (slim chance) connect and let you download.
Don't forget, you simply want the download, (watch for the little yellow alarm clock). Once its downloaded, you can go home and install. You need not sit there and perform the install.