First, thanks very much to everyone who responded to this thread. So much high-quality advice/information (both technical and practical--heck, even psychological!) offered to a complete stranger, and I truly appreciate it.
Maybe some negotiating with/bribing of my wife might be a more efficient use of time than trying to figure out how to get great sound out of small speakers in a large room.
Room correction seems to be a common theme, and @kota1's comment about being able to achieve a flat frequency response makes sense to me. Also, thanks for the Paradigm recommendation--that may be where I start, since it would be a good base for a house-wide system even if it doesn't work in the living room for some reason.
The Buchardts are appealing to me, particularly the ease with which they can be returned if they don't work out. Perhaps the wireless A500 would be a good alternative, with the Platin hub (with room correction but no AirPlay 2) or the Primare SC15 (no room correction, but AirPlay 2 and wired outputs in case I wanted a wired sub). And I've read in a few places that the Buchardt's put out a lot of sound for their size.
It may come down to personal preference, but @ddd1 might be right about the futility of using smaller speakers in the big room. I guess we will see. Those BM15A's are an interesting option. My only other thought was that maybe I could use Klipsch Heresy IV speakers as "bookshelf" speakers, since I think they would technically fit on the intended shelf space.
Thanks again.