Grover snare wires or something else?

Hey all, I have a cheap snare. That's ok because I'm a beginner. However I try make my Taye kit as decent as possible and I've improved it a LOT with new heads and tuning. On to my snare...

I moved from 2 ply to single ply batter to get a lively responsive tone. I try to go for a tasty jazz like sound and I don't hit very hard. This was better but wanting to get a different sound I bought used Grover snare wire for $15 off eBay.

It was listed as jazz bright but the winding is clearly bronze so it's one of the "dark" models. I have doubts if it's the jazz model too... Anyway it was a cool experiment. I knew it would be drier but no matter the tension, I found it gave too much drum and too little snare. I loved the reduced buzz and it was a usable sound I just wanted more of it (wetter)! Almost like I needed more strands...

I have now put on the stock cheapie (chrome plated) but it's not quite right. What do you suggest? Buy a new Grover so I get the right model or something in between the two?