Sony Hw50es mounting issues

After reading > 60 pages of the popular comparison thread, i am interested in buying a sony hw50es. However, have some mounting concerns

The room is 15x15 basement space which opens to the left to a large space 15x26 and to the back to a 10x10 space with stairs. The ambient light is minimum at night which is when i plan to use it mostly for cable, movies and rare gaming. the kids are growing to gaming may be improtatnt in next 5 years. there will be ambient light during daytime

here is the issue. i plan to install the projector in a niche (ventilated) in the drop down tray ceiling. the ceiling height is 104". the lowest height of the niche is 16" from the ceiling, so the projector is to be mounted <90" from the floor (bottom within 14" from the ceiling). the throw distance will be between 13 to 13.5 feet as the niche will end at 15' from the screen. i was considering a 110'" screen as there will be a similar drop down niche on the other side. this will allow >2 ft on either side of the ceiling

i was looking at the elite projector calculator (for hw30es) which basically tells me that i have to get closer to 120" for screen size to mount at 13' throw distance so i get within 90' projector height from ceiling. Epson/JVC are more forgiving. the 120" screen will only leave 2' from tthe bottom and 23" from the top (7" from the dropdown tray ceiling). this will be tight

here are my questions:

will it be possible to still mount the sony in such a situation?

what mount do i use. do i need a low profile?

is the vertical shift for 50es better than 30es?

should i switch to epson/jvc?

also need recommendations for screen in my setting? Budget around 1000$
have considered elite screens cine grey and dragonfly grey

need recs for surround sound system with a minimalist look? Budget around 3000$
like the look of wall mount and satellite speakers. would lik eto stay away from tower..
considering
psb imagine on wall (60 and 25 for surround)
monitor audio shadow
paradigm millenia hybrid 20
golden ear supersats (50 and 3 for surrounds)
revel M10, c10 and s12's
will it be bad (for sound quality) to have 2 wall mounted speakers on either sider of the screen and the center in the bottom. i can mount the L/R to match the bottom of the screen


thanks in anticipation

Gary

the issue is not the throw from 13'. I can throw upto 135" from 13'. the issue is i want to keep the base of the projector within 14" of the ceiling. At the same time i want the upper edge of the throw (on the screen) to be atleast 20" below the ceiling. is that possible? i believe it has to do with vertical spread/displacement. pardon my lack of correct term

forgot to mention, 16:9 screen

@jkasanic

thanks for the specs. Can you please explain how to read this spec. I am a newbie and do not understand how to read the shift range.

you understood me correctly. i would like to the bottom of the projector <14" (preferably 13) from the ceiling. so it may be another 3' from the center of the lens (overall height being 6"). it then comes out to 10" from the center of lens to ceiling. now on the wall i would prefer the top of the throw to be at 23" from the ceiling for a 110' screen. I wish every manufacturer had a calculator for this.

Gary

Thanks for the explanation. I believe you used 0.21 as an example. Is that correct? The Sony has 0.71 vertical displacement, which measures at 38"