I've been having this problem for a while now -

1)Cold, the motor starts right up.
2)If I ever turn the motor off after its warmed up, and go to start it again - it will crank, and the engine WILL start, however... within 1 second the engine will surge, and die without putting up much of a fight.
3)Restarting the motor usually requires i crank it for twice as long as usual, even pumping the gas pedal a bit.... and eventually it will ssslllowwwwllyyy start back up and run fine.

Ignition module? Ignition coil? Injectors? Dirty fuel system? Time for an LSX swap?

did you figure out this problem? I've been turning over all the stones looking for an answer to mine

I would first do a pressure test of the injectors after warmup for leakdown.
After the engine is warmed up and ran for a while, then turned off, if injectors leak down, that puts fuel into the cylinders. Upon starting the engine shortly after shutdown, it exhibits the same as a flooded issue. And as mentioned above, if you happened to "pump the gas", or hold the pedal to the floor, this cuts off fuel delivery, and the engine starts...with the sputtering as mentioned and along with the smoking exhaust.

ICM first, and injectors second, are the usual hot start suspects.

Sounds like fuel though (injectors)