12'11" is the closest the lens can be for a 115" wide screen and note the projector body is about 18" deep. Silver ticket is the most recommended entry level screen on these forums. For a scope screen power lens memory is a must so your choices are limited. A BenQ HT3550 has a shorter throw and most likely has a better 4K picture but not suited for a scope screen.
"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