IMO, a "flatter" hitter would be more affected by tension and playability loss from old, dead strings bcoz he would have less margin of error on his shots. It sounds like your crafty opponent has uncanny ability to adjust to the playing characteristics of his string set-up and his success vs you is undermining your confidence in what you rely on. If you're doing well vs other opponents it's not the equipment issues that need to be addressed. I'd work on searching for the little "chinks in his armor"...what shots he handles less easily (I hit fairly flat and don't like stuff high to my 2hbh and changing depths of shots; would that frustrate him?).
"I am easily satisfied by the very best." Sir Winston Churchill; ALLEZ ROGI!