Speakers or room

You’re screwed, big throw rug with padding beneath, heavy drapes you can close when listening, subs to compliment the speakers might have you playing back at lower volume which can tame the reflections. 

@kenjit   C'mon, one doesn't need to go 'stone cold' on the OP...he Knows he's got 'issues'...:(

Better...Rugs, drapes, plants, anything to damp the echos down...
...and keep the spouse in a 'happy place'. *S*  She might welcome an opportunity to decorate with your *ah* 'guidance'... ;)

New speakers can come later...they may be about the same amount of $ in the end as the decor but they're more likely to be tolerated 'better' later....

(After nearly 40 years, one learns how to approach such....*L*)

GIK is a good call, but....won't be as acceptable as nice fluffy rug...

Ear plugs, it will address the speakers and wife : )
Just kidding!!! Room treatment will go a long way to help and a rug would improve the sound immensely as Steve59 points out

There is no doubt whatsoever that it is the room.  Tile floors and large glass windows is tough to work with.  Curtains over windows will help along with an large area rug over the tile and lots of furniture, lamps, plants, etc.  Anything to break up the sound.  Since you talked about wife acceptance factor I doubt wall treatments and bass traps would be acceptable.  Move to a smaller carpeted room

One of the general concepts I've heard for room treatment is to treat one each of the opposing walls.  Making the wall opposite the speakers less reflective seems like a good way to start. Rugs are awesome too, + and + to above comments.Are your speakers on the long wall or the short wall?