you cant cover that section of the closet and vent into that side and just seal it well maybe hang a blanket behind.(as insulation), it will get hot in there but not as hot near the plants.
also vs. permaflect i would paint the walls white, diffused light is good light, helps with the overall intensity of the light, reflective material reflect light. meaning they continue in the straight path they where headed this mean you actually will get less light to the lower levels of the plants.(another great point to make about this is in any well designed tent you look in, it may be covered in mylar, but it is not smooth for the purpose of diffusion, you could buy specialty mylar like diamond imprinted tho.)