, there is no perfect projector for all people in all viewing conditions. Each projector has a different balance of pros and cons, and each person must weigh all the pros and cons in order to select the one with the pros that best fits their individual viewing conditions and preferences and the cons they can most easily live with. You should read some of the other threads on this forum and not try to get all of your information in this one thread.
On the 4K issue, all of the current 4K projectors <$5,000 are pixel shifters. They have fewer than 3,840x2,160 pixel panels so they can't produce 4K pixels on the screen at the same time. They rapidly shift pixels back and forth with the pixels overlapping. The best 4K pixel shifters can come very close to the performance of native 4K projectors with panels that actually have 3,840x2,160 individual pixels. But they do not represent full 4K implementation. Even the expensive true 4K models haven't implemented all aspects of 4K UHD performance yet. It's still not a mature technology.
So any 4K projector you buy today will be obsoleted by future 4K models, just as 1080p projectors will be obsoleted. The decision many are making today is whether to buy a partially implemented 4K or a mature, fully implemented 1080p model. In either case if they want full 4K UHD implementation they will need to buy a new projector in a few years. A lot depends on whether you plan to watch mostly 1080p or 4K content.
Another key element is whether you plan to view mostly in the dark, mostly with some ambient light or a combination of both. The best projectors for viewing in the dark are not so good in ambient light and vice versa. The projector models you are considering are a mix with some better for dark rooms and some better for rooms with some ambient light. No front projection system is going to be at its best if there's too much ambient light in the room. But it is possible to get a decent image with a bright enough projector if the ambient light is well managed and kept away from the screen.
Manufacturer specifications for lumens (brightness) and contrast (difference between the lightest and darkest part of the screen image) are often exaggerated and misleading. So it's best to rely on the results of professional projector reviews and the advice of experienced people on this forum who know how these projectors perform in the real world.
There are many good projectors available for <$2,000 and you've already named some of the best options. But they represent different categories within that price range and so some will be better suited to your specific needs and preferences than others. So right now it would be better to focus on what environment you will be viewing in (darker or lighter) and what content you will be viewing. That will help narrow down the field and point to a few models that would best suit you.