Resolution: ideally 1080p/2K (unless seating is relatively far from screen).
Native lens: 2.9:1 throw ratio (60' throw / 20.4' 16:9 screenwidth)
Scope lens: Add-on lens needed to stretch width to 27'; prices start at a couple of thousand $
Brightness: Screen is 310 sq ft. Movie theater reference brightness is 14 fl. 310 x 14 = 4340 REAL lumens required if current screen is 1.0 gain.
In fact you'll need something specced at 7000+ lumens (
list of suitable models) as brightness is reduced by calibration, the scope lens, and bulb aging.
Since you posted this in the $3k-$20k forum, full 2K digital cinema models are all out of budget. There is just one model -
Boxlight Pro80S3 - that comes close. It ticks all boxes except for resolution.
If your budget is in fact over $20k ask a mod to move this thread to either
the $20K+ or the
D-cinema forum - the experts there can advise.