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. Verethragna is 90.
Monk TP:
Monk VS:
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
Deluges: 288.355
Tropics: 282.672
Persistence & Depths (sphere DA 2% not counted): 281.041
Forager: 281.831
Latitude: 279.630
I set Deluges as #2 and went on to testing the 3rd:
(Base Coercion + Deluges): 288.355
Forager: 299.017
Tropics: 298.583
Persistence & Depths (sphere DA 2% not counted): 297.393
Latitude: 296.073
Eminence: 295.363
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:
#1: Coercion
#2: Deluges or Depths (for the Sphere effect and HP)
#3: Exhortation or Depths