Omnath, Locus of Mana timing issue

[TheCramp]

So I have Omnath in play, and White Sun's Zenith in hand, a bunch of mana untapped, including 3 :g:/:w: lands and 6 floating green mana. Opponents end of turn, he passes priority, I pass. Can I then tap out for green and then move to untap without them doom blading Omnath?

[cdr]

If you both pass priority, the turn is over (aside from cleanup).

If you do anything at all, tapping for mana included, he gets priority again.