Why is there even any question here?
With your w1070 at mid-throw you'd get up to / over 30 fls
On Low Lamp your still over 18 fl.
The w1070 absolutely needs some black boosting assistance, but you do not want to sacrifice your Whites.
You mention a totally light controlled room, but you also bought a retractable screen...so that seems to indicate it's not a dedicated Theater.
White or Gray, with a non-tensioned retractable screen you will always have the prospect of waves, edge curling, and / or wrinkles.
Here is a link to a Matte Gray Tab Tensioned Electric Screen. It's 119" though. But damnable affordable. $499.00
.....and a Matte Gray 100"er. You'll have to call for pricing.
Both screens would have a Gain of 0.8 so respectively size-wise from big to small, their Foot Lambert ratings using the w1070 throwing from 11'- 3" (mid throw) would be 17 fl and 24 fls
If you do paint your surrounding surfaces a Flat, non reflective color that has no Yellow or Red in it (...avoid Tan or light Brown as well...and it certainly does NOT need to be a ugly shade of Flat Black...
) then you'll have accomplished every one of you needed goals.
(...in deference to Red, if you want Red, then it must be a ultra dark, flat Red...for the walls only. Dark Gray for the ceiling...)
I suggest a neutral Light Gray...or a medium dark Blue Gray for the walls, and a 2-3x darker shade of the same color for the Ceiling.
That's my take. Now let's see what shakes out.