It’s not the distance that affects brightness, but the size of the image projected. A smaller image will always produce a brighter image.
(Moving the projector forwards/backwards or zooming the image using a lens has exactly the same results).
The inverse-square law of physics applies: An image twice as big is half as dim.
It always applies and is impossible to avoid.
I’m projecting a 92” diagonal 16:9 image using a JVC440 and I get fantastic results from HDR content - it will never be anywhere near as bright as a flat panel display, but with the right-tone mapping results can be superb.
Regards,
James.