- Get a cell phone with decent data plan and Access Point (wireless tethering), and configure the RPi-Z to connect to it instead (I would suggest, before going this route, getting a phone dealer to demo one in AP mode, to ensure you can access local clients -- ie; computer to Rpi). This option bypasses the entire public WiFi system. On second thought -- as long as the AP mode works, you could force the RPi into AP mode by turning off the phone WiFi AP... Just never configure the RPi for a public WiFi.
- Replace the RPi-Z with an RPi-3B, and then use a CAT-5 cable to physically connect to RPi. Might need to have the computer running a DHCPd; might need a small (4-port) network switch between the computer and RPi.
- Configure your computer to permit mounting the SD card from the RPi (this may need something like running Linux natively or via a virtual machine; Windows can not mount EXTx partitions). This option would allow you to hand edit the file containing the "known AP" to force the RPI into setup mode.
All IP networking related issues
Since you are relying so much on public WiFi access points, I can see three options:
Dennis L Bieber