Omnipresence, if it actually means "all" would include all times as well as all places.
My first take would be to say that God's omniscience is separate from His omnipresence that is separate from His omnipotence.
If His omniscience is a separate attribute from His other attributes, what would it mean to say that God is all-knowing?
It seems to me that omniscience is somewhat dependent on omnipresence as you defined it. By that I mean, if God was not omnipresent, then how could he know what was occuring where He wasn't. I think it's likely that if the attribute of omnipresence was removed, omniscience would suffer.
I agree with you, xzins, that the three omni's ought to be taken as independent of one another. At bottom, it would be unreasonable to suggest any restrictions on the power or person of God. Any such restrictions (such as His not being able to lie) must be declared by Him. And I am not aware of anything in Scripture which declares an interdependency of the three omnis.
A metaphor might be ye olde "ant-in-the-coke-can". It would be reasonable for the ant to perceive that an entity is holding its can (movement, etc.) - but it would be unreasonable for the ant to presume that the entity holding the coke can is also an ant.