Before getting any screen it's very recommended it be used on a wall for a few weeks to see what works.
An 160" 2.39:1 screen fits inside a 169.3" 16:9 screen. Square surface for this 169.3" screen is 85.08 ft².
16:9 needs to be used for calculations since this is the format the projector outputs and brightness goes to the black bars as well.
These measurements are taken with 100% zoom.
Zoom Lens Light Loss. Going from the widest to the full telephoto setting on the 2.1x zoom lens resulted in a little more than 28% loss of light in any given color mode.
With the current setup about 50% of zoom is used, so 14% of light loss.
To calculate the fL the lumens of the present and lamp mode needs to be divided by the square surface.
Natural preset in Eco lamp has 1438lm. 1438/85.08=16.9fL
Now take out the light loss: 16.9 x 0.86=14.53fL
After this add in the gain of the screen.
Can't remember if the Slate 1.2 actually has 1.2 gain, but let's assume that it does.
14.53 x 1.2=17.43fL
15fL is recommended for SDR, 30+fL for HDR.
Lamps loose around 25% brightness after 500h, after that the light loss is linear until the estimated hour rate of the lamp, which is 50% of it's original brightness.
The closer a projector is, the brighter it will be.
That being said, for this type of fabric and ALR's in general, in order not to experience visual artifacts a minimum throw range of 1.5x is recommended. It;s very likely that even at this throw range some artifacts will be visible with bright images. A throw closer to 2.0x would be better suited.
Throw range is calculated by the width of the screen. The width of this screen is 147.6"=12.3'.
It's unknown how much the image will be impacted by artifacts at 1.78x throw range.
Can the projector be placed further back?
You can get the screen and try the projector at different distances, with smaller images.
What are the color of the walls?
The ideal setup is a room without any reflections and a white screen. Some users are unhappy with the image of any ALR screen, without any obvious artifacts like hotspots or sparkle. But you might not notice.
While an ALR screen is good at combating ambient light, a white screen, one with maybe a bit of gain would be better. The workaround is the light should not hit the screen directly. Recessed lights in the viewing are and not in the screen area.
And for only 5-10% of sports use I would just get a white screen and manage the lightning in the room.
As to what white screen you should get, make a thread or read some of the other ones here:https://www.avsforum.com/forum/23-screens/
Of course a simple Silver Ticket/Carl's/Elite white fabric would do well.
If you want a screen with some ALR properties without the downsides, and increase the contrast of the image certain paint mixes can be used:
To read more about projector use in ambient light, check out this thread:
A general discussion on white/grey/ALR screens:
2.Use this calculator.
3. I don't believe there is any significant light output difference between the 5050 and 6050.
4. The lamp will wear out quicker if used on a higher setting. But they are not that expensive.
There is an increased thermal stress when using the projector in a higher lamp mode, but I don't know how much that will actually affect it's lifespan. If it's going to be used 5 hours every day for 10 years, that might cause some components to fail quicker. I'd say don't worry about it.
5. The mount the 6050UB is great.
Not sure how flush it gets.
Please consider treating the room for wall reflections.