Securing a Whiteboard against the Wall
Rather than using a bracket, it seems like a better looking solution
would be to predrill holes where you want these brackets in the
whiteboard and fasten the board to the wall with bolts instead,
similar to the method you used at the top.
If you feel that a bracket is the way to go, you could grab a few of
those "L" steel angles that they sell at home depot (see the image
below) and fasten to the underside of the whiteboard with the
appropriate fastener for the whiteboard's frame material. You'd want
to install about 4 of these.





Another bracket solution would be that Simpson Strong Tie also
produces a Z-Clip shown in the image below. It would be able to
resist the loads that the board would apply to it if you have
already fastened at 2 points on the top. If you can cut back the
tray and compromise on the 2" to say, 2 5/16", the Z2 would work
well for this with wood filler between the bracket and the white
board.