Don't have much else to add. But wanted to chime in and say I surrived flying with just turning 2 yr old twins to PCB Fl with a plane change layover walking outside in Atlanta first (they are 8 1/2 now) But you can do it.
We've always bought the seats for our kids, even now when I just flew by myself with our 8 mo old. But I think OP you'll be good with the extra seat.
Diito, keep 24 hr of any necessities with you in carry-on. Don't mean to scare you but...We were flying to WDW on 9-11 with those same 2 yr old twins and thought piece of cake after the first trip. Yes, 9-11 is an unforseen, but we were stranded, no luggage for 3 days, had to make a superTarget trip with that one.
Also love the diaper pack trick good one!
Make sure you carry those little disposable garbage bags for anything from dirty duds, to dirty diapers, bring a pack of double duty wipes for anywhere clean up.
And yes, check your stroller at the gate or use those baby sling things. I used cotton balls in my 8 mo old's ears, don't know if it helped but it made me feel good.
Remember you can bring liquids through security just for the babies and you get 3 carry-on's plus the diaper bag because of your 3 seats. And allow for that extra time in security of folding up your stroller and putting it through the belt scan.
Good luck and have a great trip!