4K 120" image in 10 feet with lens shift

4K with shorter than average throw is already a rare combination. Adding extensive lens shift makes it a unicorn. Is there any reason why you can't mount a BenQ HT3550 in the proper position in relation to the screen to avoid using lens shift? Aside from lacking extensive lens shift it's the most recommended projector for throwing a 120" image from 10'.

I wanted a few inches of adjustment to get the image aligned.
My mount does not go up down or left right. I suppose I could loosen the screw of the mount to the projector to shift it along the slots. Seems like a hassle. the mount does have a little tilt but I don't know how much I can tilt without skewing.
I know my image shifted when it is warmed up.

My old one (HT4050) have 2.5% horizontal and 12% vertical,
the 3550 has only 10% vertical.

I did not know it is going to be that rare.. maybe a more versatile mount will compensate for this.

I was waiting for them to make something like a HT4550 but I guess it is not happening.

When the US version of the just-announced Epson TW7000/7100 hit, they should do it. They're the newer 4K versions of the 3100 and 3700 respectively which have a lot of zoom and hefty available shift. I haven't been happy with my BenQ TK800 after replacing an Epson 3000, so I'll be very interested when these hit the states.