7.8' ceiling, 50 chairs, 120" screen too big to see whole image?

Our condo social room has a 7.8 foot ceiling.  We have 10 rows of chairs setup.

We got a quote from a vendor for a 120” screen.  (I’m not sure if that 120” was diag or width.)

If 120" was the width, at 16:9 I believe that would mean the height would be 5.6 feet.
For 119” diag measurement, that's a height of 58” (4.8 feet)  and 104” image width.

If my math is correct, even if the screen is mounted as high as possible, it would be:

7.8’ – 5.6’ = 2.2’ from the floor
Or
7.8 – 4.8’ = 3’ from the floor

Since we don't have stadium seating in our social room, my concern is that only the folks in the first row could see the whole screen?  

Since the program would be closed-captioned (with the subtitles at the bottom of the screen), most folks could not see the closed captions.

Based on all of this, what's the largest screen that would make sense?

If we mount the screen as high as possible, would that be bad from a strained neck perspective?

Thanks for any thoughts,
Mike