I do also have my own S-Corp...and did sign-up for both cards. I got the OK on personal, but a "wait-n-see" for 14 days for the business card.
My flirting w/ the SPG would be to start the process (using $ coins, etc) since Chase from what is seems closes accts when used in that way from what I've gathered in my lurking...and also to start down the path towards Lifetime Elite status on AA...I may kick that off w/ an AA credit card since I've never done any offers there...though I need to research what a "good deal" for an AA card is and not just jump on what's available right now, since it isn't critical at this point