Gnu screen or tmux in emacs shell mode: how to fix color escape codes?

[Leo Alekseyev]

I would like to attach screen (or tmux) inside emacs, in shell mode. I
often find myself running emacs with inferior processes inside screen
on remote servers; it would be nice if I could shift the workflow to
local emacs + TRAMP; ability to reattach persistent sessions is a
must, however. (Such workflow is particularly useful for analysis in
R, cf 
http://blog.nguyenvq.com/2010/07/11/using-r-ess-remote-with-screen-in-emacs/)

Shell-mode is rather desirable because I keep encountering
miscellaneous glitches and even crashes when using the combination of
M-x term or M-x ansi-term + screen + R. However, I can't seem to get
rid of ansi colored rendered as escape codes in screen when run under
M-x shell. When I use ansi-color-for-comint-mode-on, they are fine --
but as soon as screen or tmux starts, it becomes a horrible mess.

Can anyone suggest a set of conditions for proper interpretation of
ansi color with M-x shell + screen?  Some TERM=... or termcap/info
magic?..  What about getting rid of color altogether?..  Is there
perhaps an alternative way to run persistent remote processes through
tramp?..

TIA,

--Leo