Personally I'm finding that tmux+UXTerm gives me all the tmux-style screen splitting that I need. I can also "copy and paste between terminal windows and applications easily" - well, fairly easily, anyway.
To paste from the X clipboard, I need to remember to use shift+insert
To copy to the X clipboard, hold down shift while selecting the text to copy, then left-click when done. To paste that into another app, use shift+insert in the other app.
There's one area where this doesn't work perfectly: if I've got a vertical split and want to copy multiple lines. uxterm doesn't understand the split. To get around this I have "bind-key z resize-pane -Z" in my .tmux.conf; this toggles the pane between normal size and "zoomed" mode, where it occupies the whole window. C-b z makes it big, then I can copy, C-b z pops it back to normal size in the layout.