So at&t is doing something where if you already have a phone and a plan and it is NOT an upgrade/contract extension - you can just buy a new phone from them for $40? Friends wife got a new iPhone 5s for $40...
Head over to their site and try to configure that for yourself.
You can sign up for their out of contract service and pay them full price for a device,
OR
You can sign up for their out of contract service, and sign up for their "next AT&T" phone pricing (which is an ADDITIONAL monthly installment) and get an iphone for ~$40. Bottom line, You are paying more than the phone is worth no matter how you stack AT&T's chips.
AT&T is not giving away iphones for $40 outside of contract.
If you really want to stay with AT&T and have a well supported device, buy a nexus4 from swappa (~200), and grab their out-of-contract service. You could buy two of those for what you'll spend in monthly-installments for eighteen months with their "next" plan.
I know you don't like rounded devices, but the nexus android support is unparalleled, and if you're willing to wait, they are also super cost-effective. Beyond that, I'm not sure.
-sony devices are well supported, but AT&T doesn't seem to offer any.
-sIII is well supported, but is exynos, which is a tough bear on developers, so features are forfeited as a result, and it's aging. <<-
AT&T's version, i747, is Qualcomm. The
international version, i9300, is Exynos
-s4 is locked down rather well, so very limited support.
-HTC one? it's a clean, square, serious device, and there seem a decent number of 4.4 roms available therefore.
http://forum.xda-developers.com/htc-one/orig-development
If (when) this i777 of mine dies, I'll be going the nexus route ftw.
Whether n4 or n5 depends on the pricing at the time.
-happy shopping