99% sure you're misunderstanding what's going on with EG mode.I just say that the game mode works with 4K, I could not test the input delay because of the missing input delay tester.
It could be, That if i Update the Software That the EG is Not anymore working with 4K.
It's not that EG mode can't be enabled at 4K60, it's that the image projected on the wall will be downscaled to 1080p whenever EG mode is enabled.
If you go really close to you wall/screen and look at the size of individual pixels on the wall at 4K60, or icons in windows taskbar, don't you notice bigger pixels and lower resolution icons after you enable EG mode? If you do it means that your image on the wall is now 1080p instead of 4K even tho the source resolution in your pc is still at 4K.
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On a side note, i am putting up retractable black velvet curtains covering the walls and ceiling, and WOW, what a difference!! Only put 1.5 meters long curtain yet, but the contrast difference in the projection is already night and day, it makes the overall image look soooo much better!!!
Will put another 1.5 meters for a total of 3 meters, still need to get some dark carpet and darken the wall directly below the screen, eager to see results, a lot of work to put up the curtain, but it is 100% worth it and am much happier with the projector already xD