I know you're an ultra-budget traveler, but you don't have the American Express Platinum card, right? Even if you just cashed out Membership Rewards points for something like Carnival gift cards at 1 cent per point, booking your flights directly with Spirit or Frontier would net you 5 MRs per dollar, and at a low value redemption like gift cards that's still 5% back on what you say is your biggest category. Even at 100 $37 one-ways, that's $3700, which would be $185 of somewhat poor value gift cards, or $111 more than a 2% card. Unlike a standard 5% card, there's no cap here! Frontier and Spirit are both eligible choices for the $200 annual airline credit, and due to the low fares I'm pretty sure most of your airfare purchases would actually trigger the credits - and if not, the $5 "bringing your phone onboard," $12 "emergency oxygen mask access fee," etc... would be covered for sure. (And you could also make use of the lounges for free food and drinks to bring on the plane.) You would use the Uber credits, that's $200 a year right there.
Something to think about, anyway. I'm sure once you add in other travel expenses (hotels ever?) you're more than coming out ahead without even taking into account any bonuses, and it may present you the opportunity to at least splurge and reward yourself with a flight on a legacy carrier or a nicer room from time to time. You certainly qualify as a frequent traveler, so no reason the sticker shock of the AF should scare you off.
I'm just on the forums to sell the Platinum and Starwood cards. Amex should really put me on their payroll! LOL
Seriously, though, in your math you forgot that you get to choose an airline for the airline credits and that's going to be $200 in statement credits for either Frontier or Spirit in your case. Hop on it now vs 2018, and you would get the credits twice in your first membership year since the credit is by calendar year. The underwriting for the green/gold/platinum family of charge cards is the same, and tends to be below the revolving cards. I would be extremely surprised if you weren't eligible for the card. Your Experian score is about 50 points above where I'd normally say "they might approve you," and since they already approved you for a revolver...
Plus, it’s hard to put a value on the conversations you could have in the Air France lounge with your Spirit boarding pass. 
The card should be looked at as a rewards and perks card rather than the “status symbol” many think of it as, including a large percentage of people who hold the card.
The card should be looked at as a rewards and perks card rather than the “status symbol” many think of it as, including a large percentage of people who hold the card.
@K-in-Boston wrote:
Plus, it’s hard to put a value on the conversations you could have in the Air France lounge with your Spirit boarding pass.
Lololol.
A few years back I flew Spirit to another airport to fly Emirates on a ticket a client booked me on (it was worth about $7000 in their premier class but client used miles to book it). The flight attendant saw my Spirit boarding pass in the trash I was throwing out and her eyeballs got wide that I went from worst carrier in the world to one of the best, haha! Also had lounge access for Emirates and that was pretty swanky...
Amex doesn't use 1 pull for 2 cards, right? I'm at 7 on EX now after the Amex pull the other day, not sure if they're INQ sensitive, all of those are < 12 months.
Thus far in 2017, it's extremely rare to see Amex do a HP for existing cardmembers. My last HP from Amex was 15 years ago, and I got my SPG and Delta Platinum this year. DW had no HP for her Delta Gold. Also, I forgot to clarify that for December the Uber credit is the standard $15 + a bonus $20, so $15/mo except for December which is $40 = $200 annually. Unfortunately unused Uber credits do not roll over. Amex is not known to be inquiry sensitive. The $550 would be added to the first statement, yes.