Ok I see this piece in 3 different lights.
2)TP(haste aswell) Gear
3)WS Gear (yes thats right)
Ok so the Possible augments as it applies to #2 and #3 (only these because I assume you don't want Pet Augs?) is Haste+3%, DA+2%, Crit DMG+3% and also ACC+7. Now for WS Gear, it seems like they would be things all the other jobs would be going for too so why not PUP? Look at it this way:
Stringing Pummel being our shine on the Master, a 6-hit ws, depends on our acc majorly and a major focus in our gear. First off, Crit DMG+3% looks actually viable, if we feel acc is ok the +3% CritDMG to a Multi-hit WS that already has a innate Crit Hit Rate+ is already there. Second I think the DA+% is better than it appears to be. Ok, so looking at your gear, lets assume through what you tell us is 89% ACC. Therefore, you will miss 11 times in 50 rounds (100hits).
Now, I want to try looking at ACC/Hit Rate as individual hits for the time being. Saying that each hit has about a 89% chance to hit. Applying this to SP (stringing Pummel) would be (.89)(6) which is 5.34, meaning that you should hit about 5/6 hits most of the time, but 6/6 is a tad bit reachable.
Next, Lets apply Double Attack from gear. From Aesir Mantle(ignoring the Darkday effect for this, but it will make a considerable difference) you get +1%DA, Brutal Earring gives +5% (equivalent to DA trait for those who don't have one) and from the Augment you get +2%DA. The Total being +8% (+9% from DarkDay effect) thus leading us to logically apply that you will get 8 extra hits every 50 rounds(again 100hits).
Ok, Let's Apply DA to this concept. So Hypothetically according to individual hits, there is a .08% chance for the hit to be DA according to your gear. Sounds reasonable too. Now Lets apply this to Stringing Pummel. Its a 6-hit WS, so assuming that SP's hits are similar to Regular hits (your gear has no WS ACC+ so naturally I'm assuming they are Regular hits) that means that SP(DA)=(.08%)(6) ---> SP(DA)=(.48%) (w/o Augment it leaves it at .36% DA)
Now, Lets compare the Double Attack Chance. With Augment Every 2 SPs should have 1 DA, However without the Augment you need about 2.7 or rather 3 SPs (can't split weaponskills for this sry ;p) to have 1 DA occur in the WS. This is a Large difference in terms of WS's preformed to reach a desired effect.
Simply, let's see how this applies to ACC. If ACC is 89%, or 5.34/6 for SP we can see how DA will affect your WS. Now, using the 1 extra hit from 12 hits (2 SPs) we can see the hit rate for the WSs. So, 13 being the number of hits (DA occuring in 2 SPs) we just multiply it by .89 (the hit rate for every punch) to see how much it improves acc approx. The Number of hits that should land for the 2 SPs is equal to 11.57/13 where w/o the DA 2 SPs is equal to 10.68/12.
Conclusively, Double Attack adds a somewhat noticeable difference Accuracy wise the DA is basically adding a .445% to the 5.34/6 Hit Rate, boosting it to 5.745/6 hit to each Stringing Pummel. Now you may be wondering why its out of 6 hits, well this is me making the logic of how the DA possibility is somewhat like another chance to hit the 6/6 hits on SP, if you get what I mean I applaude you lol...I know how confusing it sounds ;p. But, this is why I think Double Attack shouldn't be overlooked completely anyways as it applys to WS.
Lastly, applying to WS, I like to point out the possibility through damage through /war and the Darksday effect of Aesir Mantle is another +6%. So I'm sure, through that you imagine the possibility of a total of +14% Double Attack :)
Theres .84% for Double Attack in one SP or 6 hits, or about 100% for that extra hit every 7.14 hits (lets just do 7 for sake of simplicity) ok so every 7 hits = 1 extra hit. So for every for every 7 SPs, you get 6 Extra hits where w/o the /war and Darksday Effect its 2.5 extra hits for every 7 SPs. This is true because 7 SPs = 42 hits there for for every 7 hits there is one extra, 42/7 = 6, so there is 6 hits per 7 SPs.
Ok so applying DA to 42 hits which is 48, and applying acc, thats 42.78/48 hits should land. with the other one, thats 42 hits so DA gives 45 hits, when ACC applied thats thats 40.05/45. Now lets apply both of them with the final step with Acc per ws. Now for the first one, w/o DA from augment or /war (its basically just from his gear) and 7SPs you get 37.38/42 hits. So the difference is 5.4 hits for 7 SPs (for one SP its 5.4/7) or .771 hit land for each SP. This takes it from 5.34/6 to 6.071/6 hit landed. This Proves that the DA Effect is Better than going for capped ACC because the DA allows to give DMG over that of a Full-Hit Stringing Pummel.
So Through and Through I wanted to show you the usefulness of Double Attack sry for rant.
However, I do want to say, if you are planning to use this for TP gear I just suggest you choose what you want for it, DA isn't a bad choice of course, ACC+7 is pretty good too, and of course Haste+3% is a totally acceptable option. With Haste from that, Pantin Hands, Turban and Headlong leads to a total of +14% Haste so Its up to you what you want for TP gain gear. Since you gonna use it for THF, I'd go with either ACC+7/Haste+3% or DA+2%/Haste+3% (lol an extra round (cuz its dual weild) for every 100 hits from the DA+2% on THF seems cool cuz you got TA as well on that job ;p). However the Crit DMG+ isn't bad for thf either if you use DE due to the Critical properties of Dancing Edge as well.
In Conclusion of the whole thing, if You do go for it as WS gear only for PUP(and THF I suppose), I highly suggest DA+2%/Crit DMG+ but if you want TPing gear piece only, I suggest Haste and w/e you want for Preference, if you choose DA+2% for the piece, then you might want to get either one +7 Ring for the TP set up, and if you want more acc for a WS setup go with +7ACC rings x2 for WS and just use Rajas for TPing :). But thats my Opinion thanks for Reading ^^