Funny story, my discover was opened by my parent, I had no knowledge of it until I started working on my credit and found I had a 2year old account with discover. Discover asked for my social and ID and they changed it to my correct info and i ended up keeping it.
Great job overall - I might suggest closing a few cards - Capital One, Target, and one of the Navy Federal cards perhaps. The reason I say that is, the late payments make me think you might be having trouble keeping track of everything. You don't want any more late payments, and you don't really need that many cards (not that I'm one to talk about that).
I think getting in with Amex early is a good idea, but you could wait a year or two and it'll still be early in your credit career. Good luck!
The 1st late was with my Target card durring hurricane harvey i couldnt make the payment because I didnt have an internet connection and my mind just forgot about it. 2nd was Discover, i had it on Auto pay but with my USAA checking if you overdraw a penny they will deny it so this happened without me knowing and I had another 30 day late. I have had 100% payment history since. Is it worth a goodwill? I hear that they often will not work.
I'm still confused. Hurricane Harvey happened when you were 16 years old.
As you've learned, autopay requires constant monitoring of your checking account to make sure you have the funds when the withdrawl is scheduled to occur.
Read through this thread:
The thread explains that goodwill efforts tend to entail multiple tries and getting your goodwill letters "into as many unique hands as possible." Don't give up because you've been told no.