[xmonad] How to bind w,e,s,d keys for 4 screens?

[Alistair Gee]

I have 4 monitors in a 2x2 configuration. I would like to replace the
w-e-r key bindings with w-e-s-d key bindings to match my 2x2
configuration, but it does not work. Specifically, the w & e keys
work, but the s & d keys do not work.

My code to set these key bindings is a modification of the standard
xmonad.hs template from xmonad 0.8. (My modifications are at the end.)
I would like the following mapping:

s -> screen 1
d -> screen 2
w -> screen 3
e -> screen 4

Here is the section from my xmonad.hs file. My attempt at binding the
keys is at the end.

myKeys conf@(XConfig {XMonad.modMask = modMask}) = M.fromList $
   -- launch a terminal
   [ ((modMask .|. shiftMask, xK_Return), spawn $ XMonad.terminal conf)
   -- launch dmenu
   , ((modMask,               xK_p     ), spawn "exe=`dmenu_path |
dmenu` && eval \"exec $exe\"")
   -- launch gmrun
   , ((modMask .|. shiftMask, xK_p     ), spawn "gmrun")
   -- close focused window
   , ((modMask .|. shiftMask, xK_c     ), kill)
    -- Rotate through the available layout algorithms
   , ((modMask,               xK_space ), sendMessage NextLayout)
   -- --  Reset the layouts on the current workspace to default
   -- , ((modMask .|. shiftMask, xK_space ), setLayout $
XMonad.layoutHook conf)
  , ((modMask .|. shiftMask,                 xK_space)
    , layoutScreens 4 Grid)
  , ((modMask .|. controlMask .|. shiftMask, xK_space), rescreen)
   -- Resize viewed windows to the correct size
   , ((modMask,               xK_n     ), refresh)
   -- Move focus to the next window
   , ((modMask,               xK_Tab   ), windows W.focusDown)
   -- Move focus to the next window
   , ((modMask,               xK_j     ), windows W.focusDown)
   -- Move focus to the previous window
   , ((modMask,               xK_k     ), windows W.focusUp  )
   -- Move focus to the master window
   , ((modMask,               xK_m     ), windows W.focusMaster  )
   -- Swap the focused window and the master window
   , ((modMask,               xK_Return), windows W.swapMaster)
   -- Swap the focused window with the next window
   , ((modMask .|. shiftMask, xK_j     ), windows W.swapDown  )
   -- Swap the focused window with the previous window
   , ((modMask .|. shiftMask, xK_k     ), windows W.swapUp    )
   -- Shrink the master area
   , ((modMask,               xK_h     ), sendMessage Shrink)
   -- Expand the master area
   , ((modMask,               xK_l     ), sendMessage Expand)
   -- Push window back into tiling
   , ((modMask,               xK_t     ), withFocused $ windows . W.sink)
   -- Increment the number of windows in the master area
   , ((modMask              , xK_comma ), sendMessage (IncMasterN 1))
   -- Deincrement the number of windows in the master area
   , ((modMask              , xK_period), sendMessage (IncMasterN (-1)))
   -- toggle the status bar gap
   -- TODO, update this binding with avoidStruts , ((modMask
   , xK_b     ),
   -- Quit xmonad
   , ((modMask .|. shiftMask, xK_q ), io (exitWith ExitSuccess))
   -- Restart xmonad
   , ((modMask ,  xK_q     ), restart "xmonad" True)
   ]
   ++
   --
   -- mod-[1..9], Switch to workspace N
   -- mod-shift-[1..9], Move client to workspace N
   --
   [((m .|. modMask, k), windows $ f i)
       | (i, k) <- zip (XMonad.workspaces conf) [xK_1 .. xK_9]
       , (f, m) <- [(W.greedyView, 0), (W.shift, shiftMask)]]
   ++
   --
   -- mod-{w,e,r}, Switch to physical/Xinerama screens 1, 2, or 3
   -- mod-shift-{w,e,r}, Move client to screen 1, 2, or 3
   --
   [((m .|. modMask, key), screenWorkspace sc >>= flip whenJust (windows . f))
       | (key, sc) <- zip [xK_s, xK_d, xK_w, xK_e] [0..]
       , (f, m) <- [(W.view, 0), (W.shift, shiftMask)]]


Note: I actually have two Xinerama screens stacked vertically, but I
use XMonad.Layout.LayoutScreens (combined with Grid) to create 4
screens in a 2x2 configuration. I don't think the LayoutScreens is
causing the problem b/c if I revert to using the w,e,r bindings, I am
able to to access 3 of the 4 screens as expected.