Alphalite makes flat side lit LED panels that you'd normally install in a dropped ceiling - that would have been the simple solution.
I built one from poplar. Way too much work, but I'm happy with the result.
I used two 2'x4' panels end to end. The the low voltage dimmer fits in a standard wall box. Normally I leave it cranked all the way up. If I were to do it again I'd use four 1'x4' panels providing more even coverage, but I can't complain with the 2 x 4's.
You'll have to ask Alphalite for a dealer near you.
1x4 Panel
FPL-14L/850 5000K
$82 each
2x4 Panel
FPL-24H/850 5000K
$99 each
Dimmer
WSBD010DECC1
$60
Spec sheet
Alphalite home page
Alphalite Inc. is based in Southern California and committed to developing new technology to improve lighting efficiency, functionality, and quality.
alphalite.com
The 2x4 diffuser panels are from Diamond ($50 each)