I’ve had the kit for 2 years. A human being would think to change their heads if they’ve been there for two years. I have a Remo ambassador on the batter and reso. I also have pure sound 24 strand wires which I have adjusted to your description. I have tuned up the reso head a lot and tuned the batter to whatever it needs to be. It is the snare.What exactly are you trying to get your snare to sound like? What kind of music are you playing? You keep posting all these snare questions, but haven't defined your goals.
I still say heads and tuning. I have a Midtown snare, it's essentially the same but a 5x13. I can get it to sound just like I need it to, be it low, medium, or high tunings. It has a PS3 batter and Diplomat reso. It's plenty sensitive, has tons of crack, and a nice ring at high tunings. The reso is tuned pretty tight, the batter slightly less. The wires are loose enough to still buzz at the edge, but tight enough not to rattle like a 73 Pinto.
Not trying to be rude, but I don't think it's the snare.