Looking for a stripped down version of tmux or screen
Solution 1:
I'm not aware of a "stripped down" version of tmux/screen that does what you describe, but it probably would not be hard to write one, and it may exist.
However, you can get what you want and still use the normal screen. You can do this by disabling the termcap feature that prevents your graphical terminal from accumulating scrollback data.
Add the following line to your .screenrc
to do this:
termcapinfo xterm* ti@:te@
I'm not sure what the equivalent for tmux would be, but it may be very similar.
You will have to start a new screen session for this to take effect.