[Sprint Samsung Galaxy Note 3] Real_JESRadio:
I am in NO WAY affiliated with any of the ROM developers mentioned below nor am I a developer at all. I discovered this by trial and error and decided to share with the community. I AM NOT RESPONSIBLE FOR YOU BRICKING YOUR DEVICE!!!!!!!!!!!!!!! Everything mentioned worked for me and me alone. I will NOT guarantee it will work for you. I cannot offer any support concerning why it will not work for you and NEITHER DOES THE DEVS AND THEIR VZW ROMs!!!! SO DO NOT CLOG THEIR THREADS WITH QUESTIONS ABOUT WHY THEIR ROM WON'T WORK WITH YOUR SPRINT NOTE 3!!!!!

THIS IS FOR 4.4.X ONLY!!! I am currently on NC5 baseband so I have no idea if it will work with NH7. It should, but again, I can only speak for me and my setup. SMS, MMS (with 3rd party app to send possibly) and GPS all work for me. Calls are working as well.

EDIT: Ok folks, I have decided to go ahead and post the how to anyway even though I have gotten no response from any of the devs of the Verizon ROMs mentioned below. I assume they are working on new projects and do not have time to mess with this discovery. They also do this for free and have lives to live just like the rest of us. If at any time they want me to remove this I will, purely out of respect for what they have done for all of us. With that in mind, THE DEVS HAVE NO TIME TO SUPPORT THIS SO PLEASE DO NOT CLOG UP THEIR THREADS WITH QUESTIONS RELATED TO THEIR VZW ROMS WORKING ON SPRINT DEVICES!

What you will need: A rooted N900P Note 3 device with a custom recovery installed. I am currently using the latest Philz Recovery so I cannot say for sure if using TWRP will cause this not to work on your device. I don't think it will matter, but to be safe I can only speak for Philz Recovery right now.

If you are on TWRP and want to switch to Philz (many have suggested doing so regardless if you try this or not) keep in mind Philz is not being updated now ( I think ) so the latest build for KitKat is 6.12.9 as far as I know and can be found HERE for the N900P. If you don't know how to change recoveries you probably shouldn't be trying this at all. Research it and you will find out how to do it. Or ask around. You will also need to use a 3rd party MMS app possibly to send MMS messages. On Eclipse it seems to work using the stock Messenger, but on Alliance I had to use Textra to send MMS.

Step 1: BACK UP YOUR CURRENT SETUP!!!! I cannot stress how important this is with ANY ROM flashing or file changing. I have been caught with my pants down before and it really sucks when you have to Odin back to stock because you did not do a Nandroid backup. That is the main purpose of having a custom recovery like Philz or TWRP or CWM is to completely back up your device. Most or all offer EFS backups as well. Also keep a copy of said backup on an external device in case you accidentally wipe your EXT card. Don't think it's not possible, I have done it on other devices because I thought I was cool and could wipe real fast and flash.

Step 2: Acquire the stock kernel for your build/baseband ( Mine is NC5 ) in a flashable .zip. The NCS stock kernel can be found HERE OR you can use Lean Kernel 3.10 ( which I am using) that can be found HERE. MAKE SURE YOU GRAB THE HTLESPR version!!!

Step 3: Download the Verizon Touchwiz ROM of your choice. I have successfully tested this on Eclipse and Alliance. Eclipse can be found HERE Make sure you use the correct build ( 4.4.X ) because it needs to match your baseband. In other words, if you are currently on 4.4.2 or 4.4.4 use the same ROM build that they offer. Eclipse 2.0.1 is what I am using. Alliance ROM is HERE Those are the only 2 I have tried thus far. Experiment if you dare, but the others should work as well ( in theory).

Step 4: Grab the flashable app APN Backup and Restore provided HERE THANKS TO FREEZA!!!! You will need this to get the Sprint APNs on your device. More on how do do this later.

Step 5: Take a deep breath. While still on your Sprint ROM, update your PRL and Profile for good measure because those options will not be in settings on the VZW ROMs. Relax, it will be ok.

Step 6: Boot into recovery, do a full wipe like you would any other time flashing a new ROM. Flash the ROM of choice, then flash the Sprint kernel of choice. If you do not get any errors, reboot system and wait...........and wait some more. It will take a few min for either ROM to boot. If you see the Eclipse or Alliance splash screen (boot animation) you are probably ok. Do not panic at the 3 min mark and shut down. Just let it do it's thing. You should eventually see the beginning setup screen. If after 8-10 min you still are seeing the animation it probably is in a bootloop. It may not work but you can simply power down and boot back into recovery and restore your backup, or try again flashing the kernel first, then ROM, then kernel again then boot into system and wait again. Just use some patience.

Step 7: If you made it to this step, congrats, you have booted a VZW ROM onto your Sprint Note 3. But we have more to do. After you set up wifi and gone through the setup menu you may see some Verizon related errors pop up. Just ignore them for now. Those apps can be frozen using TiBu after completely done as a cleanup measure. Boot back into recovery ( On Eclipse you will have to do this using vol up/home/power buttons because there is no 4 way reboot menu. This can be added with Xposed and Wanam later as well). Flash the APN Backup and Restore app ( this could also be done when you flashed the ROM I suppose) and reboot. which will put the APN backup & restore app into your /system/app directory and the SprintAPNxXML file onto your sdcard. Once done installing, boot back up and launch the application, Ignore the warning screen you get from first launch, then press menu and select "Disable ICS check." Once done, exit the app and load it again, then choose "Delete APNs" and select yes to the following prompt. Once done, go ahead and tap Restore APNs, and select the SprintAPNsXML from the prompt and select no to the duplicate check. IF THIS DOES NOT WORK THE FIRST TIME- Move the app from /system/app directory to /system/priv-app/ directory and change permissions to rwx/rwx/rwx and reboot. Then try to Delete APN, then try to Add APNs using the provided SprintAPNxXML file in the app. This will add Sprint APNs.

Step 8: Go into settings/more settings/Mobile Networks/Access Point Names and choose the appropriate one for your area. I chose APN2 LTE Internet n.ispsn. You should now have data icon showing. This worked for me, hopefully it worked for you. I have seen it switch between LTE and 3G so I know it is handing off correctly. Make sure Network Mode is CDMA/LTE/EVDO as well. I haven't tested on the road yet, but will tonight. But it has been working flawlessly for me on local towers.

Step 9: You will need to add Sprint apps you were using, including voicemail. Install Titanium Backup and freeze Verizon related apps if you want. Also you will notice in settings your phone will show to be a N900V instead of N900P due to the Verizon ROM. Don't panic.

Step 10: Profit! At this point you should be able to tinker with the ROMs according to what the threads offer. I know Eclipse has it's own app to customize some things. But Xposed will work as well. I have no idea if Hotspot works or any of that stuff, I do not use it. Alliance has a ton of customization settings and apps built in, including themes. Some minor tweaks haven't worked, but most have. Eclipse has actual AOSP functionality baked in. ENJOY!! I will try to answer as many questions as i can, but again, please DO NOT clog up the threads of those great ROMs with questions, the devs do not, as far as I know, support this method and will not be able to help you with your Sprint device.

EDIT: When you connect to your PC via USB for the first time you may have to toggle MTP on and off to get it to be recognized in Explorer. It will most likely say N900V when you get connected. Also on Alliance a couple of Verizon apps will try to install on your PC. You can cancel them.

Screenshots

MUCH THANKS!!!

Sprint side: Freeza for the APN Backup and Restore app as well as all you have done for the Sprint Note 3!! LMMT for the NC5 kernel thread! Phil3759 for Philz Recovery for the N900P

Verizon Side: Nitroglycerine33 for all he has done for the community. My first attempt at flashing was an Eclipse ROM. Cannot say enough about what he has done! Beanstown106 for the hard work on all the Verizon devices and now along with Team Alliance they continue to dominate!

Multiple Devices: Imoseyon for his great Lean Kernels!! I have run them on every device so far. They just get better and better.

All the devs on all the devices deserve a huge thanks from all of us! Without them none of this would be possible!!