Have you ever watch in the Cinema with the Lights On?
for your case you can use an ALR screen that can reflect ambient light but the viewing angle is very small, it is no problem if you sit at the center or close to the center.
Do you think LAMP/ BULB based projector is more suitable for daylight or when lights are on viewing? some Epson have 3000 to 4000 lumens!
try ALR screen http://bbs.xgimi.cn/thread-116587-1-1.html