I just responded to the same post on FFXIAH.com forums (assuming you are Slugman on there)
I've been wondering about this myself and just took the time to test it out on Kinematic's Spreadsheets
. I set it against Pil with Stalwarts, Chaos and Tacticians Roll, haste, all MNK/WAR JAs on and a cheap Mithkabob for food. All atamcites are tested at max upgrade strength. I used my own gearset which is a pretty standard high end Tantra +2, Black Belt, Atk/Regian Moonshade, Verethragna 90, etc. set.
Coercion quickly showed to be the best so I used that as the default #1 atmacite and here's the results for 2nd (larger number is better):
(Base Coercion): 272.679
Persistence & Depths (sphere DA 2% not counted): 281.041
I set Deluges as #2 and went on to testing the 3rd:
(Base Coercion + Deluges): 288.355
Persistence & Depths (sphere DA 2% not counted): 297.393
Exhortation: ??? (Sphere regain +2)
Surprisingly the +1 regain on Forager came out on top in the 3rd slot as far as personal DPS goes. All this should be taken with a grain of salt as stats like regain rely on TPing as soon as you hit 100% and so can be hard to judge their DPS. That said with WS procs being needed frequently in VW all that regain and store TP will be doubly useful. Also, I don't think I should have to say this but just in case: This is specific to Verethragna + VS and could work out differently with a different weapon and WS. Last side note, Forager would only need to be taken to level 10 to have the regain on it.
I included Exhortation in the last set because I think the sphere regain +2 is definitely worth looking at. If no on else in your pt has it it will far and away out damage any other choice as a group benefit that slightly weakens yourself.
You should also take into account the secondary effects some of these have. HP+15% on Depths is a very solid boost for Monk in particular. Eminence and Exhortation both have HP+5% and Exhortation also has Skillchain Damage +30%. Persistence has -5% PDT. Deluges has Enmity +15.
Based on all this my picks would be:
#2: Deluges or Depths (for the Sphere effect and HP)
#3: Exhortation or Depths