Bargain interconnects to tame treble & boost bass?

You need a new source in the worst way. Dont spend hundreds on cable while you use such a weak source.

DA DA!! Behringer DEQ2496 to the rescue again.

Seriously, its spectrum analyser will show you what your problem is, and can help evaluate any fixes you try. And, in the meanwhile you can shape the frequency response to something you like, which may not be flat at all.

A new source will help and it may be a bad speaker amp combo. I've heard that the Triangle speakers can tend toward brightness in certain setups,as far as SS goes the B-60, I used to own one, isn't particularly bright, but maybe with Triangle it is? The idea of borrowing an amp is a good one, though inconvenient, getting a different pair of speakers for a demo might be instructive as well. Good luck!

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.