In need of some MoMs monk (tiger claw/dragon style) assistance

[StreamOfTheSky]

I mean...generic bull rush optimization applies. This includes Greater Bull Rush feat and Lore Warden Fighter (big CMB bonuses). Bred for War trait gives +1 CMB, too. Or you could just build around the Shield Slam feat and get a bull rush on every attack. *shrug*
EDIT: Also, if psionics is allowed, there is psionic bull rush. You can just pick a psionic race like Half-Giant or Ophiduan (probably the best options for your build) to avoid needing a class dip for power points for obtaining psionic focus.

Then there's the critical component, where you basically crit twice on one roll. Not bad, but sadly unarmed has a 20/x2 base crit range, so it's going to be tough to really take advantage of that. Tiger Style does mean you can use the Keen property on an amulet of mighty fists (since unarmed is no longer just bludgeoning), so there's that... If you've got an ally with a keen 18-20 crit weapon willing to pick up Butterfly's Sting, that'd help.

As for getting to close to melee and take a full round action... Buy a bunch of Quickrunner's Shirts? Each is 1000 gp and 1/day lets you move as a swift. At very high levels, Mounted Skirmisher also works. You could combine Sohei and MoMS, take mounted feats...multiclass to cavalier 4 levels and pick up horse master for a mount that won't fold like a paper towel.... I don't know.

Any of that help?