4K projectors for home theatre

[New2019]

Have some old 120" screen & 3800 PJ.
Bulb was replaced just a few months ago.
Mainly watch 4K & 3D movies. Though PJ is so far so good, not really impressed with video quality (when I compare typical OLED TVs) and thinking may be I should spend more and buy a Real 4K PJs?
Any recommendations under CAD $3000 preferably?
Room setup:
Finished Basement with dark Red wall paint on sides and Black on Screen wall.
Distance between 120" fixed Screen & sitting couch - Roughly 12-15 feet
Screen bought in 2018 from https://www.costco.ca/Kanto-S71-120....100292855.html for CAD 200 and that link does not exist now. Pasted the link to give some idea.
Epson 3800 PJ ceiling mounted close to 10-12 ft from screen
Panasonic UB420 player for playing 4K and 3D discs.
No special calibration done on PJ. Just using out of the box
Attached some pics from Quiet place (new one) 4K disc and kingdom of planet of apes 4K taken with all lights off in Noon time. Basically this basement can be made real dark or if needed lights also.
Also pls see attached my default PJ menu settings for color, contrast, etc. Do i need to tweak any of these here? any baseline guide for calibration?

As i said, i like overall picture quality & no specific complaints but i do not know for sure if a real/True 4K player would make any difference or not unless i watch that in parallel as 3800 is pixel shift one not real 4K. Right?