So I applied the OTA (rooted) without the firmware to a stock unrooted version of the 1.22.651.3 ROM, and adb pulled /system. After recombining with the boot.img from the new OTA firmware, this ROM was born.
This is really just pure stock. All I did was root it (SuperSU), and updated busybox to the latest version (1.20.2). Everything else is as it would be if you actually took the OTA
I figured I'd post it in its own thread so it doesn't get lost. If someone would like to deodex the ROM and post it, I'll gladly link it here .
I'll also upload the rooted version of the OTA I used to apply the update, in case there's someone running a bone stock 1.22.651.3 that would like to just apply the OTA.
So, here we go:
Jewel 2.13.651.1 Stock Rooted (Odexed)
Stock_Rooted_Deodexed_2.13.651.1_signed.zip - 541.4 Mb(md5 0d83d69a186190b6865d00d0510462ff)
OTA 1.22.651.3-2.13.651.1 (Rooted, firmware removed) - Recovery-Flashable ONLY ON stock odexed 1.22.651.3 (with NO changes to /system)
NOTE: You also HAVE to flash either the boot.img in the bootloader or the Kernel w/boot.img in recovery after flashing the OTA file, otherwise the ROM won't boot.
If you're S-ON, with HBOOT 1.15 or higher, you will also need to first flash the boot.img in order for the ROM to boot after flashing.
UPDATE: Extracted the stock kernel as well. One zip includes the unsigned boot.img + modules, and the other is zImage only. Both require either the 1.12 HBOOT or S-OFF to flash through recovery. Otherwise, Flash Image GUI can be used to flash.
UPDATE 2: The below kernels will break Camera and/or WiFi on ROMs not based on the latest OTA.
2.13.651.1 Stock Kernel - boot.img + modules
2.13.651.1 Stock Kernel - zImage + modules