Your only other option is something like a black Diamond screen. No matter how bright the projector is your black level will never be any darker then the screen is with the projector off. You just can't fight physics, consider a TV behind the screen for daytime viewing. Don't waist your money on another projector it won't make much difference in any kind of dark scenes, it might help with bright shows like sports and make them watchable.
"Smart enough to know better, to old to care" ------ Dedicated Bat Cave Home Theater, JVC RS49U/Mitsubishi HC7900DW Projector, 110" 16:9 Jamestown screen with variable power masking for CIW 2.50:1 to 16:9, Marantz 7009 with 7.1.4 Atmos with Ohm mains,3 DIY Subs (2 15" (1 ported, 1 sealed and a 12" 4th order bandpass), 1 DIY butt kicker, Custom Built HTPC, 18TB DroboFS NAS