(info "(grub) Simple configuration") says
For example, if you have:
menuentry 'Example GNU/Linux distribution' --class gnu-linux {
...
}
then you can make this the default using:
GRUB_DEFAULT='Example GNU/Linux distribution'
However this will only get
Warning: Please don't use old title `Debian GNU/Linux, with Linux...'
for GRUB_DEFAULT, use `Advanced options for Debian GNU/Linux>Debian
GNU/Linux, with Linux 3.9-1-686-pae' (for versions before 2.00) or
`gnulinux-advanced-a0113a34-7b5e-4f63-a6d1-c566e2543350>gnulinux-3.9-1-686-pae-advanced-a0113a34-7b5e-4f63-a6d1-c566e2543350'
(for 2.00 or later)
and ones GRUB_DEFAULT, it turns out, ignored.