I'm sorry about the long delay in getting back to this (SSD with
unpushed changes was TRIMmed by Windows partition updates a few months
ago; I got distracted by other things...).  Attached are four patches.

The first avoids scrolling the phantom daemon's window by limiting the
next-window search in Fother_window_for_scrolling to visible frames on
the current terminal, as per the solution to bug#3442.  So far, everyone
seems to agree this is the reasonable thing to do here as well.

The second extends the Emacs and Elisp manuals to document
scroll-other-window-down and tries to make the docstrings of
Fother_window_for_scrolling and Fscroll_other_window clearer and more
accurate.

The third tries to simplify beginning-of-buffer-other-window and
end-of-buffer-other-window by using the macro with-selected-window.

The fourth tries to reduce code duplication in src/window.c by
generalising scroll_command to suit all three commands Fscroll_up,
Fscroll_down, and Fscroll_other_window.  Doing this made it clear that
scroll-other-window-down could also be written in terms of
scroll_command for simplicity, so this patch moves the former from
lisp/window.el to src/window.c.  The patch does not move the command's
corresponding binding from lisp/bindings.el to keys_of_window in
src/window.c because it doesn't look like any of the keys_of_* functions
can (or do) make use of the shift modifier.

Let me know how the patches can be improved,
should these proposals be accepted.

Thanks,

-- 
Basil