I'm not sure. You could try to make all settings in the taskbar on a prototype and copy the extension folder at
/usr/share/gnome-shell/extensions/zorin-taskbar@zorinos.com
and replace the original folder on the other computers with that folder.
The settings of the taskbar are saved in .js files in the zorin taskbar extension folder.
Edit: What I wrote was wrong. The user configurations are not saved in that folder so that doesn't work.
They are saved at ~/.config/dconf
So you can use terminal commands to make the changes. I need a bit time to find out them. I use dconf editor to get ideas for the commands.
You can make all settings you like and then in dconf editor (you can install it with "sudo apt install dconf-editor") go to org.gnome.shell.extensions.zorin-taskbar and take a look there. On your screenshot were not all points shown for the panel position. I tried to make it as you but I'm not sure if it is right because it was in spain.
You can try then to set those positions with a terminal command on other computers
gsettings set org.gnome.shell.extensions.zorin-taskbar panel-element-positions '{"AUO-0x00000000":[{"element":"leftBox","visible":true,"position":"centered"},{"element":"showAppsButton","visible":false,"position":"stackedTL"},{"element":"taskbar","visible":true,"position":"centered"},{"element":"centerBox","visible":true,"position":"stackedBR"},{"element":"activitiesButton","visible":true,"position":"stackedBR"},{"element":"rightBox","visible":true,"position":"stackedBR"},{"element":"systemMenu","visible":true,"position":"stackedBR"},{"element":"dateMenu","visible":true,"position":"stackedBR"},{"element":"desktopButton","visible":false,"position":"stackedBR"}]}'
To read the current value for the panel position settings after you made the settings in a prototype you can also use the terminal instead of dconf editor and run
dconf read org/gnome/shell/extensions/zorin-taskbar/panel-element-positions