looking for flat speaker cable to go under carpet

how about this :

http://www.usaudiomart.com/details/649358242-synergistic-research-dbs-30-ft-biwire-speaker-pair/

REGA FSC QUATTRO speaker cable -- Highly recommended at its price point.

The FSC Quattro can be split down the middle into two pairs of single runs; or.... left as-is for either bi-wiring. bi-amping or  a double run in shotgunned ..... it's still readily available on EBay or direct from UK on a pay as-you-go per meter reasonable price.  (unterminated or terminated) 

http://www.analogueseduction.net/category-725/rega-fsc-quattro-bi-wire-speaker-cable-terminated.html

https://www.ebay.co.uk/p/Rega-FSC-Quattro-Bi-wire-Speaker-Cable-unterminated-per-Metre/1742989008

Goertz Alphacore Veracity

https://www.thecableco.com/mi-2-veracity.html

7M terminated prices out at $684 slightly above your budget for a very nice cable.

Alpha Core is now a subsidiary of Bridgeport Magnetics.  I have a pair of the mi-2 that I will sell very reasonably.  They are certainly not mint, but 100% functional.  You know that for certain amps Alpha Core recommends the use of a zobel network, which I have and would include.

I drove an amp into oscillation because I didn't know about the zobel network when I tried the Goertz.

Goertz Flatwire is made for just your application.

Putting cables under a carpet you will pickup static and kill the sound.Good luck though!!