Hi! i think awesome wm, yes that's the name (and it also is awesome) comes close to your needs. actually, i can't believe that they did not test it. it's really popular in arch linux circles. :)
I did mention awesome, but it's so configurable I couldn't do it justice in a day (plus I don't really like it, partly because it's so configurable -- I prefer minimal WMs that stay out of my way).
On-topic, wmfs2 also has mouse-moveable splits and tabbed containers, and herbstluftwm has both manual tiling and automatic tiling modes. There are many WMs out there that might meet your requirements -- try a few!
Come to think of it, tmux uses that model too, with quite a lot of popularity, so it's not like it's a completely unknown style...
Anyone know of any X WMs that do it though? Bonus points for having independent desktops for each monitor, and also for keeping up with modern standards (compositing, that dbus-based systray protocol that I forget the name of, etc)