The only native and really 4k projectors are made by Sony and JVC and are still very expensive.
That's wrong. TI has native 4k DMDs, which you usually find in 3-chip units. Here's an example for the latest NEC (
Link). Barco, Digital Projection and Christie Digital have similar units available in various price ranges up to $750k, in case you really want to light up commercial screens for cinemas, festivals, etc.
Even Epson have developed their own native 4k LCD panels by now, here's their announcement for their latest native 4k 3LCD projector which can be used in the home theater market (
Link).
I think we have very different ideas of what "expensive" means and maybe different ideas of high quality image as well.
Sonys 4k line starts at $4k with the 285, JVCs at $6k with the NX5. I wouldn't really say that's expensive, I'd call it dirt cheap. Keep in mind those are very, very dim projectors, so nothing you'd want to use on large screens, especially not for HDR which is aiming for 1000 nits. The JVC 4500 at $35k is better when it comes to brightness, but still not bright enough for my taste (again, screen size matters alot and the type of screen fabric as well). The Sony 5000 at $60k is much better when it comes to brightness and throws a nice image in pitch black rooms with a screen up to 150" width. If you want to go bigger I'd do a double stack or look somewhere else (that is for HDR).
If 1-chip DLP is not an issue, check the new BenQ 990. Street price is below $10k and it's brighter than the JVC 4500, and a little dimmer than the Sony 5000. I'm talking calibrated lumes here, not spec sheet. On spec sheets they're all bright and do DCI-P3, which in reality isn't true.
Band for buck 'faux k' projectors provide sharp images with full DCI P3 wide color, decent (for projection) HDR performance and respectable contrast and blacks.
What's your definition of a sharp image? This depends on two things, the lens itself and the ability to resolve image detail on the chips used. For the lens, you ideally want a large lens made of high quality glass. This is something you usually find in the >$10k range. There's no limit upwards, at some point you have to be sure about your installation to actually select the type of lens for your projector. If you look at the Barco Balder, you'll see that Barco provides the choice of seven different lenses, depending on the requirements for you installation. For most of these 'faux k' projectors, the lens is a major bottleneck for resolution. I won't go into more detail, it's a well known issue. If you're interested in more detail, do a search on AVS forum, AV forums, etc. which have enough reading material for the next year including measurements and pictures.
About DCI-P3... most manufacturers claim to be able to do it, most can't, other can, but only in certain modes and with dim image. Check the color space for the Epson 4010 (
Link), it falls short of DCI-P3 calibrated. Here it is for the above mentioned Sony 285 (
Link), again failing to achieve 100% DCI-P3. Here for the $8k JVC RS2000 (
Link), also not covering 100% DCI-P3. If you don't trust reviews, get the proper equipment and do the measurements yourself.
For good HDR performance you need one thing, brightness and excellent ANSI CR. Absolute blacklevel isn't really important since HDR is all about intrascene contrast and not on/off.
No doubt one can be happy with a dim image, one that doesn't cover DCI-P3, lousy ANSI CR and so on. You can say it makes you happy, but you can't say it does all the bells and whistles. I've lived with CRT projectors for years with laserdics as source with line doublers and later quadruplers. And when Muse laserdiscs with 1125i showed up in the 90s, even with movie prices of around $500 per movie it was video heaven (anyone remember Ken Cranes Laserdisc in Huntington Beach? nostalgic memory moment here...). I wouldn't touch it with a 10' pole today.
In the end, think about what you want, do proper research, don't believe marketing nonsense and buy what fits your bill.