Looking at the drawings I know how I would do it. I would probably
use something like the Z clips on the top. But on the bottom, I would
set a piece of wood right on top of the baseboard trim and screw it
through the sheetrock into the studs.
This would give you a shear cleat that rests on the baseboard (I would
add screws to that as well). When installing, you could lift up the
piece, place it on the wall, and let it go straight down into
position. The clips would hold the top as well as keeping it from
tipping out, and the cleat would hold the bottom.
Like a good upper kitchen cabinet, I would leave a nail strip along
the bottom and screw that into the studs, too.
The one board you have for your cleat can be painted to match your
existing trim. With your cabinet at 12" of protrusion and only 8 -
10" off the wall, no one would see the cleat unless they got down on
their hands and knees.
Your width only has to be wide enough to pass your screw points by an
inch or so, meaning that the cleat doesn't necessarily have to be full
Attaching this way, you would have four screws in the base board as
reinforcement, four nice sized screws in the cleat (or more), and two
screws through the nail strip to hold the cabinet in place. All would
None would be visible with a little forethought, of which you seem to
Once again, my 0.02.