Bargain interconnects to tame treble & boost bass?

Bryston and Triangle may not be the best match out there, where both have reputation for being bright. That said, I think you really need to replace the source. Notice how the problem gets worse when you switch to the television sound via digital cable?
I have Triangle Antals 202, and my system used to be too bright with a transport-dac setup, which went away when I upgraded to a one box player.
But this might also be a a speaker placement and burn-in issue... how long have you had these Triangles? New Triangles sound "tilted way toward top-end," and the bass fills in only after 100-200 hours.
Now, getting to your question, yes, interconnects can make things better. I noticed substantial improvement in my previous setup when I inserted Acoustic Zen Matrix I, which was even bettered by Aural Thrills Active Gold. But don't forget powercontitioning/powercords, which can clean up a lot of glare.
Good luck and keep us posted.

Cardas 300B interconnects have the mellow sound that you are seeking. That does not necessarily mean that they will cure the problem.

With an interconnect you dont solve the problem. I think, you really should try a tube amplifier.

The Sony is killing you. I had one, It was nothing shy of brutal, my kids asked if my stereo was broken after hearing it. Get a DAC.

I highly recommend VH Audio "Pulsar" Interconnect. These are fantastic. Copper conductor. Very Balanced and Musical. Trial period if not satisfied can return. (I highly doubt anyone trying these would return.) I had the B60R and if the spk. is on the lean side, it is a mismatch. Consider buying a Bryston 4B ST and use the B-60R as a pre and you would be pleased w/the results. Or try to find a Brston 2B and bi-amp. Your Kimber TC wire falls on the slightly lean side as well. Try the the "Pulsars" first then decide what steps are needed next.