Hi
I have unfortunately moved to a flat with a smaller distance to the projector screen than the old apartment.
I have a ok projector frame screen of 117" (104" wide, 57" high 16:9 format so I think it is 117")
The screen is now mounted from floor: 61cm

I had the projector in the old apartment mounted 5.5m away from the screen and 2.5m high up.

Now in the new apartment it is about;
3.5 m from screen (room is 3.9m)
2.6m high

So the issue:
The projector can not scale up to fit the screen in that short distance:-/

So what do you think I should replace it with?
I have less then 30k$ in budget actually less then 20k$ if possible I don't know the progress the projector has made from HC7000 in like 12 years...)

Features I like to "keep" or to be better ( not loose if upgrade ):
+ Ultra low fan noise (19dB)
+ motorized lens shift
+ good remote throw distance
+ some good settings
+ trigger input
+ contrast level
+ at least the same picture quality

Features I like to leave behind (and level up, from a upgrade):
- better lens shift for my need
- better Ansi
- more nits for my conditions
- more setting abilities


Features I like to have IF possible:
+ 4k (I hope..)
+ led/laser lamp (I can always which.. )
+ some new cool things (?)

So please don't recommend a 90k$ projector ??

Any ideas ?
(New or old