For what is it worth. I have been dealing with this issue for a year. Phone exchanges, a Stack of SIM Cards 5 inches tall. LOL. Nothing has worked. I have performed the factory resets and done all the cookie cutter fixes that Verizon has asked me to do. This was after the 5.0 update on my Note 3. So did an experiment and flashed my phone back to 4.4.4 KitKat. Guess what? I have a lot better phone service now. The problem is GooglePlay (the new version) breaks the apps in KitKat. Forcing you to upgrade back to 5.0. So I did a clean wipe, cleared all the partitions and reloaded with the 5.0 version that comes on the Verizon upgrade assistant for the phone. Phone worked nice for about 4 hours, then apps started locking up again, phone overheating, dropped calls, Roaming, no service in my house, download speeds were 3g. Verizon exchanged the phone with a note 3 replacement. Same issues, runs hot, no signal, dropped calls, roaming at random times. Needless to say I know this phone inside and out now. Thanks Verizon for forcing me to be a expert on this device. 
. So one last experiment. I went to AT&T and got a SIM card. Installed it into my Note3. I have not had a dropped call since. The downside is I can only go 3G with this Verizon phone on the AT&T network because its not compatible with their towers. However, my battery life has doubled. I have service everywhere now, apps do not hang anymore. Thus leads me to the conclusion that there is an issue with the Verizon network. They want me to buy a new phone to fix the problem. I have several friends in town, (Amarillo, Texas) who bought new phones in hope of resolving the mentioned issues above. They have the EXACT SAME PROBLEMS with the new devices, and a new 2 year contract. They are royally [removal required by the Verizon Wireless Terms of Service] off. When I bought my Note 3, 3 years ago the service was awesome. I had service where AT&T did not. It would appear the table has turned and AT&T got their [removed] together and has the better network now. I would maybe suggest you try the AT&T sim card and see what your results are. You can get one and try it for 3 days and return it at no cost if it doesn't work out for you. I will warn you that the Verizon phone nags you about not having a Verizon sim card installed. IF you press an hold on that notification and press stop service button, it will go away until you reboot the phone, then you simply have to kill that process again to get rid of the nags. It will work in 4G H+ data mode, 3G, 2G, and 1X on the AT&T network. Just no LTE. What is sad, the 4G AT&T service is faster than my LTE Verizon download speeds. Food for thought. Do with it what you will. I am waiting to see what the Note 6 brings. If it is a sealed unit with no Sd memory card, then I'll get a note 4 and go to AT&T. I have been more than patient. I also bought my mother a S4 for Christmas two years ago. Her phone was great until 5.0 update. Her battery won't last more than 4 hours now in standby. Her phone is slow, and drops calls. Sound familiar? I don't think it was the 5.0 update. I think it is a combination of wireless drivers, and the network. The network doesn't like the "handshake" and boots the phone from the network and then it reconnects. This constant handshake and negotiation of signal is overworking the processors in the phones and thus straining the battery, causing the overheating issue. I am probably wrong on my theory but I have a good feeling I'm close to the root cause. I have been trying to root cause this for a year. Samsung when you call them, Bless their hearts, ask you to take the phone to a Samsung Kiosk at Best Buy and let them "Flash" a "Fix" for you that can't be done on a OTA update. Problem is the closest Kiosk to me is in the Dallas area, only a 6 hour drive one way. Yeah, that's going to happen. LOL. Anyway, Sorry to be the bearer of bad news. But as much as I hate to do it, looks like AT&T is the answer for now. In 6 months I am sure Verizon will get their act together when they loose market share, or get a class action lawsuit filed for misleading customers into buying new phones to resolve a "known" problem. I would hate to be a Verizon phone rep that takes these calls all day long and has to lie to the consumer. My 2 cents on the problem. Verizon, I'm so sorry you have taken this path. (Oh yeah, I forgot to mention you get unlimited everything on AT&T with rollover data, and 5GB of data for 89.00 a month. ) No contract. I'm paying 87.00 here for 3 GB of data and no signal.