If by triple dip you mean hitting the airline credit 3 times - I assume you mean waiting for the annual fee to drop, then when the calendar year switches you get the new credit, use it, then cancel the card within 30 days of that fee having dropped so that you get reimbursed. Personally I think you're playing with fire there, it's not the same as the double dip because since your 13 months (30 days after 12 months) must span 3 calendar years, you'd have to open in December then can close it the following January (13 months). Since your first year actually ends in December, I'm sure Amex won't take kindly to using a credit during the grace period of reimbursing your annual fee, then requesting your annual fee back on the grounds of the card "not providing value"...as you're actively trying to snake an extra $200 in AA gift cards.
If you want to legit milk it some more, hit the Saks credit a third time and hit the Uber credit a 13th time but open it in December so the Uber credit that's doubled is the $35 December credit. You'll get $500 + $285 that way. Not as good as the $500 + $400 you're looking for but this way is more legit (and efficient). Note I'm not saying what you're talking about definitely will get you in trouble with Amex, it just, to me, sounds like a good way to try to do that.
Hell if you *really* want to milk it get the Ameriprise plat, do all the above, then open another plat and close the Ameriprise - consider the Ameriprise year a giant sign up bonus
