Second system recommendations $5K budget

This may stretch your budget a bit, but I recommend that you consider a Lyngdorf 2170 integrated as your foundational piece.  They will go for about $2500 used.  The internal DAC is really good and the room perfect software really makes optimizing set up in a room easy. It will drive most speakers very nicely. The Lyngdorf, in my opinion, is head and shoulders above what I expect from Class D.  It doesn't really sound like tube, nor does it sound like what I expect from SS.  Somewhere in between perhaps.  I have one in my second system in a room with problematic accoustics and it made a world of difference.  You don't say what you intend to use as a source, but the high end input module gives you plenty of coax, optical, a USB, and even an internal MM phono inputs. the DAC is good enough that you can probably get by with a decent CD or DVD player using the Coax or USB input.  This thing is good enough to warrant stretching the budget a bit.  Used, these things are an insane value.

If you’ve owned Harbeth and liked them it seems like a no brainer!

If you're looking at Buchardt s400 just go for the a500 bundle while it's on sale. 

Ye Gods! What is your "Main" system?

This is your third system? And still you're asking for help? Here??! Good God, man! And you said the bedroom is 12x12? Clearly you need GIK professional consulting. Are there windows? Where? Can they be moved? Treated? 

Surely you can see where this is leading. It can't be done. I would just buy a new house with proper dimension bedrooms.