When we happen to have a monitor that still uses the VGA connector instead of the DVI connector where monitor identification can be probed, it then all defaults to a paltry 1024x768 display resolution, even though the monitor can do 1600x1200 if we let it.

There is no /etc/X11/xorg.conf to edit. There are lots of other X-related folders and files that seem kind of complicated, but none clearly to do with my main aim.

How exactly does one set the display resolution in a Mint 17 Xfce distro, in a way that sticks?

At the least, how does one increase the poor set of options to choose from, when using the GUI tool?

Nearly all search answers involve getting at xorg.conf, which is not something to be simply created from nothing when much of the job is being done in other ways - or at least in different locations.

The usual hiding places are
1. There might be no Xorg.conf, but xorg.conf.d in /etc/X11
2. Xorg.conf might be in /etc/X11
3. The other place is /usr/lib(64)/X11/lib/ or subdirectories.

By default debian based systems don't have xorg.conf. msut be run from console window manger must be stop or in single user mode.

Not sure about the rest of you...

this answer does absolutely nothing for me and doesn't make any sense.

OK, translation:
There is no default xorg.conf but you can create one by using xorg's own configure option. To do this you must be root, and X must not be running.
So boot into single-user mode and run the command xorg -configure. You can edit the file that is created for you, then copy it into the /etc directory.