Ctrl-ALT-F2 would take a miracle to work. Shift does as you describe, but the net effect is still nowhere what is intended.
Also note I am the same user. The functionality I want is how byobu behaves with screen. eg you can start 3 xterms, in each one run byobu. And each one can jump around as they see fit all sharing the same screen session. No work, no fuss and exactly sane.
The tmux behaviour baffles me. I can't understand why anyone would want all their viewers to change in sync. Short of a classroom demo environment, it really doesn't make sense as a default.
I'd be delighted if by default byobu did whatever was needed to make tmux behave usefully.