Well people advices are always...as intended to be.
I mean, you must see the result with your eyes, not just "white, quite lot lumens so grey it is"
My jvc has a real 1300 output lumens. I must say in eco of course (and with almost all iris closed) it's absolutely enough bright for me, more than 50 nits on screen which is perfect.
But the point is, yu can have even 6 millions of lumens but with a grey screen you will always see dark whites and dead colors...it's not a matter of ambient or lumens, it's always a matter of in what you are going to project, the image is "created" there. And the grey (for me at least but you can see with your eyes)is absolutely never a good point to be used.
My suggestions is to take a great contrast projector as jvc for ex and a good white screen. Grey is useless even in ambient like ours (white walls ecc).
Take a less good projector and a ALR screen...
As i'm going to do...
Take a jvc with not a lot of money (i sold my rs2 for 450 euros and took this RS46 for 520, so basically 100 euros i put on) and a ALR screen...the result is more or less an oled big screen
Cant' do any comparison now, i'm waiting for a cinegrey 5D and will post then...I tried the 3D nad the result is absolutely stunning on one way, but poor on brightness. That's why i then chose to see a 5D with more gain...the ALR screens unifies basically the grey pros with white pros screens. expecially in our environments...