How can I move the run as admin option out of the more tab?

Make a copy of the shortcut to your application.
Right-click on the copy, select Properties, Advanced and set the Run as Admin checkbox, OK, OK.
Then right-click on the copy again & select Pin to Start.

Do check both shortcuts work as expected. I have a vague memory of somebody, after having tested the run-as-Admin-shortcut version, having the problem of the application then running as Admin whichever shortcut was used. I never understood how that problem happened but thought I should mention it.

Denis