7 with Synchrony??? What was the time frame of getting all 7? I would be very anxious that a blue envelope may hit your mailbox, especially if you got CLI-request crazy on any of those cards.
Since there's so many folks who did get the blue envelope/account closure with overexposure to Synchrony, I'd be looking carefully at the apps you do -- too many apps in a row may force Synchrony's hand when they SP you in the future.
Amex makes sense, because even if you get a $2000 SL, you can get it to $6000 after 61 days and $18,000 after another 181 days. That would likely cover any losses in case Synchrony sends you colorful mail.
No chance for Chase without an offer if you're over 4/24.
Is your personal loan your ONLY loan reporting? If so, paying it off will drop your score significantly.