Here's an update for anyone who finds this and is in the same boat.
I had two issues: 1) the power button became so recessed that it's a hassle to turn on/off the screen, 2) the phone kept turning on and off, by the end almost constantly, without any obvious pattern beyond it getting stuck after me touching the screen (i.e. never just up and turned off while being idle).
Because of the recessed power button, T-Mobile shipped me a replacement phone. Should arrive tomorrow.
I still tried troubleshooting the rebooting issue. I think it came down to one or a couple of the following:
1 - Go Weather EX
2 - Freeza's CRT mod
3 - flashable 1% battery mod
4 - bootanimation.zip support flashable script
5 - something in the Deodexed version of the stock KitKat rom
In prepping to take the phone to T-Mobile, I did the return to stock thing with Odin, putting back stock kitkat odex non-rooted rom. The entire afternoon I got not a single reboot. Since I came back home with the phone, I restored a backup I had made before doing the Odin stuff. Back to rebooting.
So I thought, let's go back to the stock experience like I had earlier, and restore my apps through the play store and manually hunt it down.
Now i'm running the stock odexed kitkat rom, rooted, with lean kernel, with a whole bunch of stock apps frozen, and virtually all my apps and not a problem. I avoided 2-4 since those mess with the framework and I thought it could have something to do with it. I removed Go Weather EX because I experienced a reboot once while setting it up as a live wallpaper.
When the new phone arrives tomorrow I'll try to duplicate my current setup and hopefully won't have any more rebooting issues. I hope this helps anyone experiencing the same thing. I know it's kinda convoluted and not very concise, but then again this experience has been nothing short of annoying and confusing.
HTC Wizard -> HTC Evo 4G -> HTC Evo 3D -> Samsung Galaxy S3 -> Samsung Galaxy S4 (wife) -> Samsung Galaxy Note II -> Samsung Galaxy Note III