Integrated Amplifiers with neutral sound

Isn't SIM the amplifier that Totem, (like Fritz?), uses at trade shows? When you say SIM sounds to analytical, I wonder of what you really would like is a tube integrated or a Class A integrated - like the PASS INT30. How much power do you need to drive the speakers? How sensitive? What kind of impedance characteristic?

For $5k and for smooth jazz I would consider Rowland, Pass and perhaps MBL.

This might be overkill as far as power needed, but its smooth, detailed and great bottom end, fits your budget and will drive any speaker in your future.
Coda CSIb

I second Timlub's recommendation. I have had my CODA CSi for about 4 years and still love it.

My Exposure 2010s2 sounds phenomenal with my warm Castles. Entry level Simaudio in it's place sounded too warm and sluggish (though I do have a Simaudio CD player).

That's well below your limit though. In the same vain as Exposure, I would try LFD. Never heard an LFD amp personally, though. Only read about them.