Some finer points:
My car smelled of gas strong from the rear when it would start.
But mine (when flooded from sitting for and hour or so), would not start up for a few secs. Then it would run rough till it burned off the gas. Would not catch and then quit like yours.
So I guess it's worth considering as leaky injectors would not necessarily manifest themselves as the exact same set of symptoms.
I'm curious to know what solves your problem after you get it sorted. Please come back to explain.