[INFO] Locked Telus S4 (i337M) [4.4.2], unlocked (with AWS) on JFLTE-GPE [5.0.1] topic

Device: Telus S4 (i337M)
Start: Locked on stock KitKat (4.4.2)
Finish: Unlocked Telus S4 (i337M) on JFLTE-GPE 5.0.1 (thanks Danvdh)
Confirmed on: WIND and Rogers

Disclaimer: Proceed completely at your own risk. Please seek support from the cited threads.

Notice: None of the source information, software, advice, goodies, anything... none of it is mine. Credit belongs to the brilliant minds that have spent countless nights creating these scientific works of art. Bravo and hats off to you incredible people.

Step 1 - Starting from scratch - supplemental GUIDE (thanks veryluckyguy)
1) DOWNGRADE - Odin flash stock TLS 4.2.2 - supplemental GUIDE (thanks samersh72)
- Note: trips KNOX
2) ROOT - using Odin with CF-Auto-Root (thanks Chainfire)
3) UNLOCK - with RegionLockAway (thanks again Chainfire)
- Note: Do not perform the service menu thing (NV Rebuild...) it re-locked my device
4) ENABLE AWS - with AWS MOD (thanks zaryan)

Step 2 - Moving on up
1) UPGRADE - Odin flash stock 4.4.2 (thanks 0mega1)
- Note: Odin FAILed at 1st, do not unplug/reboot the device, wait and retry after the device reconnects (~5 mins)
- Note: resets KNOX, removes root
2) ROOT - using Odin with CF-Auto-Root (thanks Chainfire)
3) RECOVERY - flash TWRP with ROM Installer (instructions)
- Tip: Install APK with "My Files", CHECK the box for "Unknown Sources" in Settings > Security
*OPTIONAL* confirm that all features work (talk/text/data/wifi), reboot into recovery, make TWRP backup

Step 3 - The big leagues
1) FLASH - Pure Nexus 4.4.4 (thanks Danvdh)
*OPTIONAL* confirm that all features work (talk/text/data/wifi), reboot into recovery, make TWRP backup
2) FLASH - Google Edition 4.4.4 (thanks again Danvdh)
*OPTIONAL* confirm that all features work (talk/text/data/wifi), reboot into recovery, make TWRP backup
3) FLASH - GPE 5.0.1 ROM (honestly thank you Danvdh)
*OPTIONAL* confirm that all features work (talk/text/data/wifi), reboot into recovery, make TWRP backup

After 4 days of trial and error, in the end these steps worked for me and I sincerely hope they work for you.