VV atma and Cruor buffs Auto Cap your FSTR, also RR and Cruor Buffs will do the same to your ACC.
Adding more STR to your already Capped FSTR will not compete to 2% Double attack in any way shape or form.
Altho as long as you are still maintaining your proper X-hit Sword Strap is still the reigning champion, same goes for Rose strap if it is pushing your x-hit.
The best grips at this stage in the game for most melee are Sword Strap if it doesn't mess up X-hit, Rose Strap if you need it for X-hit, Pole if the above is false (Claymore is decent if you have a crit WS). This grip is not one of them.
Those who say this grip is superior to any other grip forget that rose strap bumps many weapons to their next x-hit build easily without sacrificing much.
I would agree with Itachi that Rose Strap is better in cases where the 4 Store TP would bump you up into your next tier. I would also add, however, that with magian trials and other equip Rose Strap is no longer needed for War to reach a 6 hit build or a Drk to reach a 5 hit build. (/sam) I would say in those cases this grip would be the better alternative.