looking for an integrated amp in the $1500 range

Look at Musical fidelity M3i  ,  very good amplifier.

Try an Allen Eaton tube amp (no need for pre), and a pair of caintuck audios fast 15 - that setup is slightly over budget but man will it sound magical at low to mid volume levels. Great combo.

Higher sensitivity speakers. Will make the biggest difference, especially if your looking for a $1500 integrated to fix your problem. Your 400's are rated at 87db, which means they are probably along the lines of 85db. I've never heard your 400's but with those specs I would imagine you need to turn it up a little to hear all the details, dynamics, and bass on the same level. Lower the volume and you are missing a couple quality's of the loudly played music.

If what I'm describing is the issue you are having then I think you should look for higher sensitivity speakers. If what I described is not really a problem for you then spend your money elsewhere. Good luck 

Call underwood Wally , the Audio GD line has very good value ,and Walter 

owns the Peach tree Audio line and May Ave something  close to your budget 

if you can stretch to around $2k  it would be much more feasible and much higher quality parts. You dont want a $20 Alps volume pot it robs resolution .

a relay controlled ,or resistive ladder is much better.

I had a Rogue Sphinx 3 paired with multiple speakers. I loved the hybrid design and thought it sounded quite good. While traveling for work I got a Peachtree Decco integrated. I was amazed at how good low volume sounded. It was a small apartment with low celings unlike my home. I ended up upgrading to the Rogue Cronus Mangnum III. Low volume is a dream but out of tour price range. I would look at the Sphinx and compare with a Peachtree. TMR usually has both used for under $1500. Good luck.