For those who might be wondering what problem may be caused by the "4K shift", it's called wobulation. The matrix used for the projection is not 4K, it's 2716x1528 for example, but there's a "quick" movement of it to simulate more pixels that there really is, therefore it simulates an UHD picture. So for me, it would be similar to flicker or dithering, pixels moving really fast and using the persistance of vision to create the picture. This method is way cheaper than a native 4K matrix.
I only know about one native 4K UST projector, it's the Sony VPL-VZ1000ES, which is really massive and expensive.
Of course, there are many native 4K projectors now, but they may not be UST