I am glad you checked all of the keys. This does have the classic symptoms of bad SKREEM. Since PIZZAGUY knows the entire start sequence we might need a refresher. Pure logic and process of elimination still come back to the SKREEM. Here is why; the third try and no crank. If this were some other component the SKREEM would register the key as good and continue to let the car try to start but since it is disabling the further attempts you have to look at all the SKREEM does to prove it has the correct key and is able to tell the rest of the starting process to continue past the 3 tries. IE, bad CPS still allows the user to crank and crank and crank as many times as needed but no CPS signal no start. No fuel pressure no start but cranks like mad. Etc. Etc. The 3 tries and done point TO the SKREEM.

Did you perhaps swap the key antenna for the FOB unlock/lock antenna at the SKREEM? Not even sure if that is possible with connector types.

Does your trunk have water around the locking module? It may tell the SKREEM there is a fault kick the user from starting.

Rodents in the car? That will do weird stuff!

I am certain this is the SKREEM telling the car to stop the starting process but it's some external component telling it to. (like swapped antennas)