lpatron, thanks. There was no mention of a 50,000 signup bonus on those links, but I'll take your word for it.
I just signed up for both the Amex and Visa. 100,000 miles would give me enough to get to PPT. Now all I have to do is receive the cards, spend $6,000, wait for the miles to show up in my account, and then hope there is still award availability on AA to PPT. Simple enough.
I think this has a pretty slim chance of working out, but at the very least I'll have 100,000 more AA miles when it's done for another trip.