looking for an integrated amp in the $1500 range

I found that low level listening was best done with super quiet gear. I had a lot of success with Benchmark AHB2 and LA4 preamp for that type of listening. Music details at low volume are not obscured by noisy gear.

Now if you want to skip the low level requirement but in the same physical space. Get a RAAL SR1a earphone and have 2 channel sound at any volume level in your space. I listen to the SR1a or CA-1a (not 2-channel sound) late at night, such as right now, when everyone is sleeping. Listening to Led Zeppelin now and it is as loud as I want it. I am using a Schitt Aegir amp for this ($800).

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.