You have set a sub $1,000 budget for a room in which you intend to teach professionals about something on a regular basis and you have extreme requirements for the setup of the room and an unusually large screen size?
Not one bit of that makes sense to me.
At 150" in a blacked out room, the GT1080 may do okay, but with any lighting on, you will be lucky to achieve a 5:1 contrast ratio, and colors will be weak.
You need closer to a 4,000+ lumen specification for that screen size in a dim room, and you want that post calibration, not by manufacturer specifications.
If you are part of a tech company that is paying people $60,000+ a year ($30/hr) and you have 20 of them in the room, then that's $600/hr. for their time. Yet, you have a budget that is basically the cost of ONE HOUR of their time. I expect you want to get hundreds of quality hours out of the projector you install, so I would recommend that you might want to discuss with someone the possibility that perhaps your budget is just a smidgen too low.
Then you have the issue of the ultra short throw requirement and screen size which is extremely atypical for short throw models.
Knowing the short throw requirement now and the screen size you are after, then this is the list I would pull from, and I would specifically avoid the cheaper DLP models which won't touch their claimed specifications:
While there are some $7000+ models on that list, and some $2,000- models on that list, the vast majority are between about $3,000 and $5,000. I would take this list to management and let them know that THIS is their budget they must meet to have acceptable results.
I would be very comfortable recommending this model to you, which is just under $3,000:
You would need their short throw lens to go with it (as you would pretty much any projector on this list that is acceptable)...
Which is CRAZY expensive. So, maybe a bad choice in projectors.
From Epson... http://www.projectorcentral.com/Epson-Pro_G7000W.htm
With this lens: https://www.bhphotovideo.com/c/produ...Zoom_Lens.html
So, about $5,000 total vs. $7,000 for the Sony setup.
Be aware, that the Sony with a more typical throw lens is likely closer to $3,500. But, your requirement for the lens to be really close to such a large image increases cost significantly.
NOW: Would the GT1080, or (better) the BenQ HT2150ST be usable? Yes - if you completely black out the screen area with no lighting at all and use a screen with a bit of gain to it like 1.3-1.6 or so. You would have acceptable results for not a lot of cash. The HT2150 can't be as close, so it may not work, but it is actually brighter with colors than the GT1080.
Others may chime in with some recommendations as well, but I would seriously look at budget.