Well, if the "Move Tab to New Window" is placing the new window on the primary display, even when your Safari window is on the second display, then that's probably a bug in the Apple Safari Menu item. Of course, with KM we can usually find solutions.
Which OS do you have? If you have Sequoia, there may be a simpler approach that your attempt above.
In either case you still have to move the window from one screen to another. I think you will find the answer to that problem in the following thread. In that example, it's possible that you may get better results if you change "Back" to "Second."
I'm not sure if this advice is a complete solution to your problem, but think of it like turning you in a better direction.