Probably not. If you truly have a 119 club head speed, and only carry it 257 that means that the problem lays in your attack angles. You do not hit your driver on the upswing and this produces back spin. For me, who is a plus 2 handicap, I find that though the shaft is somewhat important, it does not lower spin drastically, only launch angle. I'd check out your attack angles on trackman and try to get it to the optimal 4-5 degrees of up swing on the way through.

Thank you very much got a fitting next week to take a look at the attack angle with a trackman and a secondary look at shafts.

Getting fit helps dramatically. I have similar swing speed as you but no longer have the problem with spin. Just upgrading to a quality shaft blind won't help. Go and get fit.

You need to see a qualified Titleist fitter, at your swing speed, according to Trackman data SS 115 you should expect to carry the ball around 280 with good contact & properly fitted driver. Typically players with swing speed over 110 see better results with X flex shafts

Matt has given you some excellent advice regarding seeing a fitter. Getting on the trackman and trying different shaft is worth the time and money.

I am a 2 hcp and ss of 111 and was using the same shaft in my 915D3 and would carry about 270+ but spin was a little high @2800-3000. I recently got fitted for the 917D2 with the Rouge Max 65X. My spin has dropped to @2100-2400 and I gained about 10 yards carry, but my consistency of ball flight has been the greatest improvement. I fitted mine with the 12g draw weight and have just a nice little draw now.