Recommendation for an audiophile speaker cord that is not "bright"?

Going from some generic twisted copper cables without terminators to a $2000+ per meter speaker cable is quite a jump. You should experiment more in the low end before you take the plunge. Who knows you might find something you like along the way.

Like others have mentioned I would avoid all plated cables for now and stick with pure copper. All of the plated speaker cables I tried either sound too bright or harsh with my system (YMMV). I would also try some solid core cables instead of the usual stranded construction. Get a pair of the Audioquest Type 4 "no frills" cables audioadvisor sells and see what what you think. For me they improved the bass and low end punch vs a simple twisted stranded pair. They also had a pleasant midrange and I didn’t notice significant brightening in the treble.

Considering the amount you are willing to spend trying it should be a no brainer. You can get an 8 ft pair with bananas for $110 shipped. Then if you like it work up the Audioquest solid line. They should have the same voice.
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I'll add a third recommendation for Analysis Plus Cables . In searching for cables I first looked for a company with Proof of function and genuine science and engineering . And yes, I was impressed NASA chose their speaker cables for a special project they had .
 After that I saw AP's solo crystal interconnects were most highly recommended and their silver oval 2 speaker cables as well as the larger big silver oval speaker cables had highest approval . I do not find their silver speaker cables bright with my open baffle Spatials and the solo crystal ic's are just magical . That does it for me . I cannot imagine better than what I have now for cables . BTW , balanced connections with XLR are the future of high-end sound , IME . Pro level . I don't believe in using cables for tone control .
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cguitargear777  vendor on EBay    Used can also be found in the usual places .

"There is complex interaction among amp/speakers/speaker cable. "

Nothing complex about this, it is all about opening up so the amp can breathe freely. And there is only one way to do it right, hook up some thick solid core copper conductors..
  How much is enough? No power-conductor on the secondary site should be less than 9awg on smaller systems, 7awg on a fullrange system. Bi- and tri-wiring opens up a good system quite a bit.

OldHvyMec, you`re on the right track with your thinking. 

And your reasoning for 7awg?  ... any idea the resistance of a voice coil? How about the variation from one speaker to another?  Does length of the run come into play at all?

This is hand waving with little to no justification leading others astray.