Higher end value cables

I also have the DH Labs BL1, and it's a good interconnect for the money but not really what you're looking for sonically.  Although not absolute, I generally agree with your instinct to go with copper interconnects given your stated preferences.  Reviews of Morrow cables seemed to sync with what you're looking for sonically, which is why I recommended trying them, but Dorkwad preferred Darwin and Teo so they may be worth a good look too.  And yes, this is like opening Pandora's box, but it's a worthwhile effort that will be an interesting learning experience and reward you significantly in the long run.  And hey, wires are about the easiest components to ship and flip, so at least there's that.  Not to start a controversial sidetrack here, but I think you'll find those that say wires make no difference are, um, different.  Unfortunately in this hobby absolutely everything makes a difference.  In fact, ironically, this may be the ONLY absolute in audio.  Again, best of luck and enjoy the journey!  

Ah.  Sorry I misread your post.  So, just for reference and now that we know what you're looking for, what interconnects and speaker cables are you currently using?   It just helps to know what your current reference is to help make better recommendations. 

That said, in my experience you're looking for a tough combination of traits at that price point.  Off the top of my head and if I'm you, I'd demo some Morrow Audio MA2 interconnects and maybe also SP2 speaker cables.  You might be able to strike a deal with multiple cables as well and very low risk to demo on your system, which is invaluable.  I'd be surprised if you're disappointed, but if you try them make sure they're broken in before making any firm judgements.  Again, best of luck!

If you know which aspects of sound reproduction are most important to you and/or know areas in your system you'd like to improve, read some reviews to see which cables seem to excel in those areas.  When you find one or two that seem interesting, just buy some used cables and give them a shot.  If not a big improvement over your BJC you can likely sell them at little or no loss and move on.  Some usual suspects would be Acoustic Zen, Audioquest, Synergistic, etc. 

Another route would be to try those manufacturers who sell direct and offer in-home trial periods.  Morrow, Triode Wire Labs, Grover Huffman, etc.

Hope this helps and best of luck.