Speaker system

If you have a large room like this, you must live in a mansion.  That said you will have a difficult time filling that room with sound.  If you can afford a room that size in your home, you can certainly afford a larger size system.  That is a huge room.  Perhaps install a system with speakers in the ceiling to hear music throughout this room.  Not sure how to image a sound stage in such a large space.  There are a lot of very knowledgeable people in this group to get advice.  Perhaps include a picture of the room you are working with.  Perhaps, find a smaller room in your house to set up a listening room.

A large 1980's vintage boom box...

A butler to crank it would be an extra expense.

For such a large space (hospitality?) and the stated budget you will most likely be better off to start with a Public Address (PA) system.

If you have a "Guitar Center" nearby you could consult them (they carry self powered Bluetooth speakers).

If no "GC" then look for a local pro-sound company.

DeKay

You would be better served looking at a pro audio site.

i.e.Yamaha or QSC powered speakers with 15inch woofers and possibly a sub.

Altec Lansing VOT solid state amp and solid state preamp.

You may want to divide the room if possible. I doubt if you will be experiencing any type of sound stage. That may not be that important.

BTW I have Yamaha DSR 15's ,2 FOCAL CMS subs that I am controlling with a Benchmark DAC 3 HGC ,OPPO CD player and Cambridge sound streamer.......Sounds great outside for party's or large indoor rooms ...I am not saying this is to die for. It sounds a lot better than you would expect of a PA system.

Good Luck