Disappointed w/ Klipsch Heresy III. Now what?

The limited placement options are your challenge. In my experience, for low volume listening, if you cannot play with placement, you might try dipolar or bipolar speakers. Those are more airy in a greater variety of listening positions.  Less sweet spot oriented. Problem is those need to be out from the wall.  My Maggies are wonderful low volume speakers.  But the wife never goes in that room...

Also, Roon has some DSP and room correction features you might play with.  

That said, babies make a lot of noise.  Headphones for the next 3 years, then try again.  Your utopian idea of everyone in the living room talking and you still listening to music at high fidelity is very sweet, but if that happens for 10 minutes per day you're doing better than I ever could with the family.  Best audio in my life during that period was in the car!

I don't believe it's your speakers. While they won't Image like the Ohms, the resolution can and should be outstanding. I had Klipsch for 25 years. I also had a Rega Brio  and experienced the same dull sound. The Klipsch LOVE tube amplifiers. I recommend an amp from Decware. They build to order and the price is great because they ship direct and cut out the middle man. Call and talk to Steve Deckert. He knows his stuff. 30 day trial and a lifetime warranty! You can't lose!
Best wishes, Jeff

Brooklynluke, I have owned a pair of Heresy IIIs for several years. I pair them with a McIntosh solid state preamp/amp setup and use Nordost interconnects and speaker cables. I will offer a few comments.

Firstly, not to offend but letting WAF dictate everything you do with your system is a sure route to disappointment. I have the same concern with my wife’s disapproving comments regarding the look of the components in the room, the visible wiring, etc. But I have found it necessary, while honoring some of her requests, to be insistent with regard to my audio needs. I find that if I explain why the speakers/compoonents need to be where they are and involve her in the conversation, she will slowly relent and after awhile I hear no more complaints.
Secondly, my H3s did improve over time, but I think that after 100 hours you should be getting most or all of what they have to offer.
Third, you are allowing everything but sound quality dictate your speaker placement and orientation. I believe that a 10’ spread between the speakers is just too much. Six or seven feet apart, with a slight toe-in would be appropriate. If you point them directly at yourself so that you are looking directly down the axis of the horns you will experience harshness. And a good seating position would be 12 feet or so from the speakers.
Speaking of harshness, Art Dudley wrote a review for Stereophile a few years ago in which he basically liked the H3s but found them too harsh in the high frequencies. I’m sure you could find this review is still online.
Third, my personal experience with cables and interconnects has shown me that the do indeed matter a great deal, and that more expensive does not necessarily mean better. To a certain extent they act like tone controls, accentuating some parts of the spectrum over others. I found that some of the lower priced Nordost cables worked better for me than the more expensive ones and yielded a more balanced sound. For me, the choice was more detail but less tonal fullness with the higher priced cables. I tried to go with 12 gauge braided lamp cord for my speakers, hoping that this cheap hardware store solution would give acceptable results. What I got was a smeared sound that was unacceptable.
Fourthly, I think you may have mis-interpreted one of earlier comments someone made about using risers. He was talking about using the risers that are already supplied with the H3s to tilt them upwards. You seem to have interpreted his comment as a recommendation to get speaker stands. I have not tried aftermarket speaker stands myself. If you do, I’d like to know your results.
Fifthly, I do find that a subwoofer is needed with the H3s as well as with every other speaker I have owned. The H3s are only good down to about 60hz, and they start dropping off way before that (above 120hz). I have a 15" Velodyne that I position in the corner of the room.
Well, that’s about it for now. If I think of anything else I will post it. Good luck!

Do you have the opportunity to try them in a different room?  High efficiency speakers really benefit from boundary reinforcement and if you can't get them to "lock" into the room you will never get the sound you want. For years I have had a set of Cornwall's that I never used much. Often thin, tinny with washed out bass. Much the sound of what Ralph describes with phase issues. A few years ago I moved and fired up the speakers in the new house.  Enormous difference, top to bottom and almost the opposite of what I had experienced. I bought a pair of ALK crossovers ( Wall Scala which can be used with Heresy I believe) with taps on the mid and tweeter to further dial them in. Now they sound completely even, coherent fleshed out, almost creamy and at all volume levels. If they don't work with the room I doubt equipment changes will help enough, but the ALK crossover is killer. 

Have you tried pointing them slightly upwards? You simply place something underneath the front feet/spikes of the speaker to change, somewhat slightly, the vertical direction of the speaker. It will be very hard for your eye to ever pick up the slight change you have effected but I had somewhat the same problem and this helped. Acoustics can be nearly as important as the speaker itself as I would imagine you known Changing the focus of the speaker can work magic in some instances, one of which being clarity and definition at low volumes. Good luck.