What is your budget? Does the 4K to 7K include the screen? Does your room have complete light control? What size and type of screen are you considering? How far from the screen will you sit? These are some of the considerations that influence your decision. AVSFORUM has an active Display Devices section including over $3,000 and under $3000 projector forums.
As a few have mentioned, JVC and Sony are generally the manufacturers considered for a quality Home Theater Projector.
Sony just announced a couple new projectors so you may find some used options for owners that like to upgrade often. I wouldn't go back more than one generation for used and would want native 4K support.
JVC hasn’t released anything new for a couple years but are still favored by a lot of users. I have owned JVC projectors and currently use an RS-JVC 500. It can play 4K and HDR content but is not native 4K as the current RS3000/NX9 - JVC RS2000/NX7/N7 - JVC RS1000/NX5/N5 models are. If I was to upgrade I would go with the JVC RS2000/NX7/N7. I also have a Lumagen Pro processor that adds a lot of cost but can really dial in a calibration and has excellent Dynamic Tone Mapping.
For longer HDMI cable runs consider RUIPRO Fiber Optic HDMI Cable, Supports HDMI2.0b,4K60HZ, 18Gbps Bandwidth, HDR10, Dolby Vision (various lengths from 6m to 30m).