In the Dependent Origination formula, shouldn't perception precede craving instead of feeling? In the paticcasamuppada's formulation of the twelve nidanas, vedana precedes tanha. 

As far as I currently understand, vedana is just the physiological and psychological -and involuntary- response 
(felt as a pleasent, unpleasent or neutral sensation) to an specific stimulus. Vedana by itself shouldn't be an enough condition to give rise to tanha, because there's no necessarily an evaluation (sañña) of that feeling that could lead to the rise of a preference (like, dislike or neither-like-nor-dislike), and consequently, to the rise of tanha.

If read in this fashion, shouldn't be sañña placed between vedana and tanha?

Thanks in beforehand.
Vedana and Sanna are conjoined not disjoint.
When it says Vedan it implies there is Sanna as well.

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"Feeling, perception, &amp; consciousness, friend: Are these qualities conjoined or disjoined? Is it possible, having separated them one from another, to delineate the difference among them?"

"Feeling, perception, &amp; consciousness are conjoined, friend, not disjoined. It is not possible, having separated them one from another, to delineate the difference among them. For what one feels, that one perceives. What one perceives, that one cognizes. Therefore these qualities are conjoined, not disjoined, and it is not possible, having separated them one from another, to delineate the difference among them."

https://www.accesstoinsight.org/tipitaka/mn/mn.043.than.html