I am sorry to hear that you are completely dissatisfied with the LG Envy Touch. When I had the phone I was happy with the limited features it had and experienced a few freeze ups and random restarts. It was nothing to get me pissed off. One thing that was promised but never delivered was the avaiilibility of apps. When my contract with Verizon ended, I reluctantly gave up on the phone and moved on...
In your situation you can get yourself a replacement phone through eBay or Craig's list. Practically any Verizon phone will do. But make sure you get a phone that does NOT require any additional services to your plan (such as the Unlimited Data Plan if you don't already have one). You're going to have to buy the phone outright so don't expect to get the phone at "with contract" prices. Make sure you know the retail value of the phone so that you can compare and get a good deal online. You're also going to have to check to make sure the ESN number is clean on used phones to get on Verizon's network.
When you get your replacement phone, you can either activate it yourself by calling a number or go to a Verizon store to have them switch phones. There should not be any charge for this service... if there is then you can try to complain OUTLOUD what a POS the LG Envy Touch is and how "You guys aren't doing s*** about it so you had to buy a replacement phone yourself" etc..., talk to a manager, or just leave and try another Verizon Store. Basically just give them hell, LoL.
The replacement phone should NOT affect or extent your original contract since you are NOT getting a new phone with Verizon under a "with contract" price. The service plan is what you agreed to. Nowhere in the contract does it say you have to use the LG Envy Touch during the entirety of the contract
I know you probably didn't want to spend a dime getting a replacement phone but if the LG Envy Touch is being such a pain than I believe this is pretty much the only solution for you.
Hope this helps!