I would suggest getting a low lag 1080p unit for gaming, possibly one with HDR support and a dedicated 4K unit for 4K BD/streaming content. If you use a painted wall (i'd suggest a light grey paint) it would be relatively easy to set up the projectors.
You could get a HD27HDR and a UHD50 (or refurbed W2700), for example, and stay in budget. The UHD60 has too long a throw to work, given your placement requirements.
You could get a HD27HDR and a UHD50 (or refurbed W2700), for example, and stay in budget. The UHD60 has too long a throw to work, given your placement requirements.