@OP. Sorry, but you are asking for the impossible in terms of a bookshelf speaker sitting on a cabinet in a space of that volume if you want actual hi fi as opposed to background music.
That said, probably the best compromise you could get in terms of sound quality is to put a pair of quality two way monitors from the likes of Harbeth or Sonus Faber, or a on good stands as far away from the side walls, and listen in the nearfield. BTW, if you can accommodate floor standers, surely you can accommodate a smaller speaker on stands - they have the same footprint.
One other alternative would be a pair of planar dynamics, but you'll want them further from the front wall than you are planning.

