[Sprint Samsung Galaxy Note 3] Sesquipedalian:
I wanted to confirm this works. I am running on T-Mobile with OC Lollipop stock. I used Odin 3.07 for my flashing. (3.09 uses two letter codes that confuse me!) Here are the steps in the order I did them:

0) Backed up all data with Titanium, then a nandroid just in case.

1) Inserted T-mobile SIM and powered on phone, had invalid SIM message

2) Power off

3) Boot to Download Mode

4) Run NAB one-click full stock restore (it's an .exe that has ODIN built in)

5) Boot normally, power off

6) Boot to Download mode

7) Flash MI3 Modem (from first post) in Odin PHONE slot, unchecked Auto-Reboot

8) Wait for Odin to display RESET! then unplugged phone and powered off by holding power button for 8 seconds

9) Boot again to Odin and flash MI3 modem a second time, leaving Auto-Reboot checked

10) Allow phone to boot, them power off

11) Boot to Download mode

12) Use odin to flash TWRP recovery in PDA slot, uncheck Auto-Reboot

13) When Odin said RESET!, unplugged phone and powered off by holding power button 8 seconds

14) Reboot phone into Recovery to load TWRP and let it initialize

15) Flash Chainfire SuperSU

16) Reboot phone phone to System from TWRP (normal boot up)

17) Run SUU.apk to apply international unlock

18) Follow instructions in the first post to apply domestic unlock (including build.prop modification and creating an APN)

At this point, I can stop and I have a clean NAB with MI3 modem setup, of course I confirmed everything worked before proceeding. To get from here to Lollipop, I did these steps exactly:

19) Power off phone

20) Boot to TWRP Recovery

21) Perform the normal wipe (data, cache, dalvik)

22) From TWRP, choose to reboot to Download

23) Flash OC5 stock tar in PDA slot of Odin, left Auto-Reboot checked (you could always do the double flash here, but since it takes so long, I didn't!)

24) Allowed phone to boot and received Invalid SIM error

25) Power off phone

26) Boot to Download mode

27) Flash MJ4 modem using Odin, unchecked Auto-Reboot

28) When Odin says RESET!, unplugged phone and held power for 8 seconds to power down

29) Boot into Download mode again

30) Flash MJ4 modem a second time in Odin, leaving Auto-Reboot checked

And that was it. I booted up into OC5 Lollipop with MJ4 modem and no bootloops. I think the key is to have the phone configured correctly to use only GSM/WCDMA (UMTS/HSPA/HSPA+)/LTE configurations. The bootloop is caused by the phone trying to register on CDMA. It may also be important to wipe data from TWRP, then boot to immediately to Download mode when flashing the OC5 tar.

If you do get bootloops, you can flash the OC5 modem and they should stop, though you will be getting the invalid SIM message. You can then tinker with your settings, and flash the MJ4 modem again and see if the bootloops stop. I want to say that you if your phone is in airplane mode, the bootloops also stop.

I would imagine that, with OC5 firmware on MJ4 modem, this is a stable setup that will allow any of the Lollipop custom roms that are flashed through recovery to preserve both SIM unlocks and not cause bootloops. I am exhausted from getting stock OC5 to work, so testing custom Lollipop roms will have to wait a day or two.

That said, AT&T and T-Mobile are both deploying LTE in the 1900 PCS spectrum. For LTE, that's considered Band 2. Our phone supports Band 25 LTE, which is a superset of Band 2. So if you are in an area with Band 2 LTE from AT&T or T-Mobile, you should be able to use it. It's probably only a 5 MHz band, not particularly exciting, and possible not even faster than HSPA+, which I find to be just as good as Sprint's LTE in my area! It makes me wonder why I have been using Sprint at all. Falling back to 3G is just awful -- EvDO is slow enough, but often the phone blatantly lies and you're really on 1xRTT (technically I guess that's 3G, but most people would consider it 2G). RIP CDMA2000 and 3GPP2, you will not be missed. I have joined the dark side!