So, no seamless changing of zone
Nope, because every Playing Now is tied to the Zone it is playing in. You could consider the Playing Now list as being inside the Zone, so what you are asking for would be to seamlessly move the Playing Now contents from one Zone to another.
Ctrl+T toggles through Zones, as an alternative to the Toolbar button.
Your Link and Unlink process is probably the quickest solution now, particularly if you want to stay in the same View.
Another alternative would be to open a tab for the current Zone, leaving the View in the original tab, then select all the files in Playing now, or a subset of them, then right-click on a file and select "Send To > Play (Zone name) > Play (from here)" or one of the other play options. If you have MC set to "Start playing when files are added to Paying Now", then playback would start in the new Zone. You could leave the original Zone playing, or stop it now, and playback would continue in the new Zone.
As to your request, if a "Send To" function was added to the right-click menu on a Zone in the left Navigation Bar, then I guess you could send the contents of the Zone to another Zone. Then playback could begin in the new Zone, and you could stop it in the old Zone. Details of the transition would have to be worked out. Maybe by default it should send all the remaining tracks to the new Zone. But what would it do with the Track currently playing? Maybe sending it along with the current playback position would be possible. As you are using a function in the Navigation bar you would never have to leave the View you were on. But you would still need to switch Zones in order to see what was playing in the header, if you stopped playback in the first Zone. You would also have to switch Zones after stopping playback in the first Zone. The other option would be to "Stop After Current File" in the first Zone, but would playback start in the new Zone immediately? Or should it work like Linking the Zones, and then Unlinking, so effectively moving playback from exactly the current position to the new Zone, and switch Zones at the same time? So maybe instead of using a Send To function, create a "Move To" function, which does it all automatically?
So I guess if this is a feature request you might want to say exactly what you want MC to do, given the above issues. If you specify it well, JRiver may actually do it.