I use the orphaned Ion as my window manager, and I love it. Here’s a Lua function I wrote for Ion that handles directional movement across frames with multiple screens (ie multihead) the way I want.

First, if I’m on a frame at the edge of a screen, and I try to move to the next frame, it will move to the closest frame on the next screen in that direction. This is based on goto_multihead.lua in the ion3-scripts package.

Second, the normal frame movement functions like ioncore.goto_next() just traverse the tile hierarchy, so frame movement is sometimes unintuitive. For example, if there are four frames in a two by two grid, and the bottom left is selected, moving up could move to the upper right instead of the upper left. This function fixes that.

function my_goto_multihead(ws, dir)
    -- determine which edge(s) of the current workspace we're on, if any.
    local edges = { left = false, right = false, up = false, down = false }
    for d, v in pairs(edges) do
       edges[d] = not ioncore.navi_next(ws:current(), d, {nowrap=true})
    end

    -- cross to the next screen if we need to. (note that this is only supports
    -- screens next to each other horizontally, not vertically.)
    local fid = ioncore.find_screen_id
    local nxtscr
    if dir == "left" and edges.left then
       nxtscr = fid(ws:screen_of():id() - 1) or fid(-1)
    elseif dir == "right" and edges.right then
       nxtscr = fid(ws:screen_of():id() + 1) or fid(0)
    end
    if nxtscr then
       ws = nxtscr:current():current()
       ws:current():goto()
    else
       -- actually handle the move. may wrap around.
       ioncore.goto_next(ws:current(), dir)
    end

    -- try to preserve the edge we're on, if any.
    if dir == "left" or dir == "right" then
       if edges.up and not edges.down then
          move_all_the_way(ws, "up")
       elseif edges.down and not edges.up then
          move_all_the_way(ws, "down")
       end
    elseif dir == "up" or dir == "down" then
       if edges.left and not edges.right then
          move_all_the_way(ws, "left")
       elseif edges.right and not edges.left then
          move_all_the_way(ws, "right")
       end
   end

   if nxtscr then
      move_all_the_way(ws, dir)
      -- need to move once more to wrap around for crossing screens.
      ioncore.goto_next(ws:current(), dir)
   end
end

function move_all_the_way(ws, dir)
   while ioncore.navi_next(ws:current(), dir, {nowrap=true}) do
      ioncore.goto_next(ws:current(), dir)
   end
end