Hi Chuck. If the sun coming in is that strong, you could use a 50 - 60 % shade cloth and not have to worry with the blinds. IF the phals still seem to get too much light, just move them inside of the cattleyas. Most likely the window glass is multiplying the light and causing the burns. I prefer the black shade cloth over the silver and shiny or green varieties, but suspect it really doesn't make much difference as they are practically the same. IMHO. Black is just less jaring to the eyes for me.
I hope others will chime in with their opinions on your question.