Finding a balance between Brightness and contrast is important. The darker / deeper the blacks are without your whites / colors being affected, the more dynamic the image appears.
Of course for those without the experience to know the difference, this can be very subjective. Also, while a Gray surface can and will give the appearance of deeper black levels, this is a "off the screen" effect, not any actual change in the PJs performance.
In your situation, the Flexi-White will absolutely satisfy your desire for brightness, however color saturation is dependent upon Contrast to a great degree. The depth (richness) of color can be judged by the graduating range of shadow which relates to perspective...the appearance of an increase of the depth of field.
A Bright image can look "bright", yet look decidedly "Flat". A projector with 500,000:1 Contrast has a huge range of difference between the Darkest and Lightest element within an image, so any "Color" will have a wider gradient between the area "closest" to the viewer, and any part that recedes deeper within the image. A Projector with 15,000:1 Contrast, not nearly as much.
(...in retrospect however, compared to older PJs that spotted 1500:1 Contrast, 15,000:1 ain't so bad....)
Consider a human face....the nose and cheeks being forward of the ears. You would expect (hope)that you could see depth by noting that there is a gradual deepening of shadow as the facial surface curves away from the front. the deepening shadows give the appearance of depth...a 3D like effect.
All this relates to how a surface will either assist or retract from a PJ's ability to deliver a dynamic image. You want to use Economy mode, but at the same time use a 135" screen. The two are not being conducive to achieving an effective balance between lumen output and foot lambert of reflection. Now while reducing lumen output and foot lambert can give the appearance of darker blacks, every other aspect of the image is also darkened. That equates to a loss of dynamic imagery.
Using a white surface with 1.2 gain (Flexi-White) would assuredly let you use Economy mode with negligible effect on dynamics, however there will be no ability to increase the appearance of color saturation or contrast. Whatever the W1070 is capable of delivering will be all you can see. And that might just be enough...or more than enough for you.
The room however now comes into the equation. With a big screen, and knowing the size of most Flats (apartments) in Eastern Europe, if the edges of the screen are close to a adjoining wall and/or ceiling, the amount of light reflecting off those surfaces (...from the projected image...) will affect the Contrast on-screen, washing out colors and black levels to some degree. If you had Contrast to spare, this effect might be too little to notice. You do not have such however.
So back we go to a Grayer surface. A light Gray such as the Flexi-Gray, when hit with higher lumen output, first attenuates those Lumen s, and in doing so deepens Black levels. The primary advantage being that comparatively, you do not see a similar reduction in Color dynamics because Gray has the effect of also deepening color satiation. Therein lies the reclamation of your advantage... in normal lamp mode and with a Gray screen, reflected light coming back and hitting the screen surface meets with a higher degree of resistance. Both the Black levels and Colors have further to go to be reduced to a point that visual quality is grossly affected.
All the above pertains to one using a No-paint, Screen material only application. The Screen coatings we have developed on this Forum focus on achieving more gain...or maintaining gain, while also deepening Black Levels without a corresponding loss of Whites / Colors. To that effect, most acquire a White substrate, either a solid material or a surface like the Flexi-White, and apply a special paint to it.
Which brings us back full circle.
BW is a sub-1.0 gain paint. You can achieve that level of performance by simply using a Gray material such as the Flexi-Gray.
Or you could use Flexi-White as a substrate and paint one of several varieties of coatings, a few of which would be ideally suited for your screen size and desired lumen output (econo). Those choices would provide varying levels (shades) of Gray, but augment the Gray with additional gain-enhancing components. Some are simpler that others who are more complex....all require spraying. But the end results are always commensurate to the effort and expense extended.
Lastly, you can go with Flexi-White alone, and run the PJ on Eco, examine your results, and still upgrade to a Coating if you find the situation less to your liking.
On this Forum, many such as I don't aspire to giving "...just get by..." advice. That is why some must suffer long replies such as this one.