Data point
I applied for two AMEX credit (not charge) cards on Monday. One was instantly approved and the other is still "in progress".
Customer service rep said if you apply for two cards in the same day, there is an automatic 3-5 day fraud prevention hold by the system that cannot be overridden. Not sure if that applies only to credit cards or if charge cards also have the same limitation. I suspect the former since others have posted approval of two charge cards and/or one charge and one credit in the same day.
Rep said when the hold expires, the application will then be processed. He didn't know if there would be another hard pull or if they would use the one from the initial application. Said that is determined solely by the automated system and could go either way.
The hold should expire today or tomorrow. Hoping for approval without another hard pull. We'll see.