I realized that some of the spillover light can be caught by reflection off the inside surface of the glass, and by reflecting from the light fixture reflective surfaces. So, I sketched this to see how that might work:
It looks promising, to me, at least. I then priced the heat sink required to keep the LED's cool. That would be a one foot long piece of 5 3/8 wide heat sink, cut along the centerline to make two 2 5/8 wide pieces, placed end to end. A single 120 mm cooling fan mounted above this should keep the heat sink cooled. That adds another $35 for the heat sink and about $20 for the fan.
To power the LED's, drive them, I found a 40 volt DC unit - it takes about 29 volts for the LED's in series and 700+ mAmps of current. This is the unit I found:
http://www.cdiweb.com/PortalProductD...x?ProdId=23479 for about $20.
So, the total cost of parts would be about $150. So far, so good.