Not sure if this helps you or not but I was able to install Zorin 12.1 without using keyboard from the live desktop. After reading your post I decided to give it a try just for a challenge. Whether your KB works once installed I have no idea but steps below if you want to give it a shot.
I assume your mouse works as it seems you got part way through the install process when you discovered no KB.
Was going to suggest using 'on screen keyboard' but after attempting this myself I couldn't figure out how to make it stay on screen and it only seemed to appear when I pressed the Menu (Swafy??) however I did manage to install by using on screen KB the follow way.
Boot Zorin up to the live environment, click the icon next to the clock go to settings (the cog), Zorin Appearance, choose the far right hand side "layout' close that window, next while still in Settings main window, Universal Access and scroll down to "Typing" turn on Screen Keyboard exit Settings and start the Installer.
When text input is required, click the Activities menu top left corner and click into the search field that appears top middle of screen and the KB should appear at the bottom, type your name then double click it to select the text and right click to 'copy' , click Activities menu to close it and right click and 'paste' into name field etc, if an unwanted 'computer name' appears just triple (3) click and then paste over it.
As I mentioned this was just a personal challenge to see if I could do it as in the past I have had some very unusual problems and even stranger solutions to them. The reason for changing the "Zorin Appearance" is the default menu blocks part of the keyboard.
Linux eXspert: Where "X" is the unknown and "spert" is a drip under pressure.