Thanks.  On my first restart attempt, setting desktop-restore-in-current-display to t seems to have enabled me to restore as expected (unless by coincidence I was given the same display as the last time - I didn't check).

From: rgm@gnu.org At: Apr 15 2015 14:03:51
To: Richard Munitz (BLOOMBERG/ 731 LEX)
Cc: 20247@debbugs.gnu.org
Subject: Re: bug#20247: 24.4; Emacs hangs at startup in desktop mode

"Richard Munitz (BLOOMBERG/ 731 LEX)" wrote:

> Some more information. This problem could be related to tmux. The last
> time the hang occurred I noticed that my environment settings had
> different values for XTERM and DISPLAY. Currently they look like the
> below, but on that day they were different. Unfortunately, I don't
> remember which was which. But the .emacs.desktop file had one of the
> two values and it hung. When I edited the file and changed it to the
> other of the two values, it started flawlessly.
> XTERM=/usr/bin/X11/xterm -ls -sb -sl 4000 -display sundev28:37.0
> DISPLAY=sundev28:37.0
>
> Of course I don't understand the internals, but I don't understand why
> emacs starts up and tries to use a saved "display" value at all? Why
> doesn't it just always use the display value defined in the current
> shell in which I am invoking emacs? Perhaps this is sometimes
> desirable, but is there a setting I can use to make emacs ignore this
> value saved in the desktop file and always use the value from the
> current environment?


Maybe setting desktop-restore-in-current-display to t will help?

I suspect that in that variable's doc:

   If nil, restores frames into their original displays (if possible).

the "(if possible)" part is going to be tricky to get right.

See also http://debbugs.gnu.org/17693#40