ironass
Extreme Android User
Because you seem knowledgable I have two queries:
There's your first mistake... believing that I'm knowledgable!

1. Any idea how I can re-root my Samsung SGH-I337 running Android 4.4.2; Kernel version 3.4.0-2539008 Build KOT49H.I337UCUFNI1?
Rooting the U.S. devices is different to rooting the 98% of worldwide phones and this query might be better addressed in the (AT&T) Galaxy S4 - All Things Root forum. I believe TowelRoot is the preferred method on some U.S. editions but you should really check for your particular model.
2. Once I accomplish that, could you recommend a custom ROM that is up to date? I'll have to spend a week or so reading tutorials on how to flash my ROM before I actually try it, but it's good to also read up on potential replacement ROMs.
There are, in the International forums, 2 main types of custom ROMs. The TouchWiz based ROMs that closely mirror the look and functionality of the Samsung stock firmware. Then there are the AOSP ROMs, such as CyanogenMod, that more closely resemble the basic Google Andriod, Nexus, firmware and do not have any of the Samsung add-on's.
Once again, you will need to peruse the (AT&T) Galaxy S4 - All Things Root forum to see what ROMs are suitable for your variant.

