This may be a viable solution, you'll have to give it a try and see:
- This answer uses Safari as the browser, change as needed.
- The Service1 was named Collaborator Keystroke, change as wanted.
- The keyboard shortcut assigned to the Service is ^`, change as wanted.
For the Automator Service1:
Use the image below for the settings.
tell application "System Events" to keystroke "]" using command down
For System Preferences > Keyboard > Shortcuts > Services:
Note: Sometimes with an Automator Service1 and assigning a keyboard shortcut, you may first have to trigger it from the target App's Services menu one time. From then on the keyboard shortcut should work normally.
1 In macOS Mojave an Automator Service is called a Quick Action.