So - I am not sure what you removed from your plan as a whole, however there are directions from Verizon bundled with the new phones saying what to do if you have poor sound quality/reception.
Step 6 in the quick start guide says "Turn on Advanced Calling" and also has a warning "As a first generation service [..] calling experience may differ..."
Anyhow - to turn it off is per the directions you gave (and also included in the quick-start guide). The new service is to allow Verizon iPhone users to have both voice and data usage at the same time without requiring wifi. Basically, what AT&T and T-Mobile have been offering their iPhone users since day 1.
Settings > Cellular > Enable LTE > Voice & Data (the new first generation that may cause issues for people)
If having issues change to:
Settings > Cellular > Enable LTE > Data Only
The guide says nothing about changing anything on plans to modify this.