So I have been talking back n' forth with a Verizon rep (who is quite rude), via text/chat, and they aren't making it clear why I should keep 4G LTE on while on Safety Mode. Just out of curioisity, I turned off LTE in my settings menu, and only started to use 3G, and it works perfectly fine. It's slower than LTE, but all my apps and websites load.
I've included screenshots of the chat, but essentially, this is a marketing tactic by Verizon. The rep told me, they do not recommend I go off 4G LTE while on Safety Mode, because I should be purchasing a data boost, using WiFi or upgrading my data plan. They claim that using 3G "tricks the system".