Just limit your Navigation mesh so that it only goes left-to-right. You'll have to give it a slight bit of height (for the raycast to be able to "see").
I think you need to make it very very thin vertically. Just make it go where you want it to left and right but only make it a very small amount in the y direction.
I think that's going to be too thin - as we've suggested, give it some height. If you have no need for "up/down" animations, just assign left and right animations as the up/down - that way if the character is stopped mid-turn, he'll always be facing sideways.
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