The location that you moved to, is it in the same general area you previously lived? Have you viewed the coverage map in your new area? There are several factors that can degrade your service, such as terrain, large structures etc. What is the zip code where you're currently residing? How far do you have to travel to get better service?
I have moved to a wooded area of Whatcom County WA. Verizon thinks I should have 4g coverage. If I go down the mountain about a half mile I get decent coverage. Verizon seems to think if I buy their extender ($250) and connect it to a hard wired internet connection it should solve the problem. I think that Verizon should pick up some or all that tab! Am I a dreamer to expect Verizon to do this? Been a Verizon customer for many years.
The bad thing is, if you lived higher than the tower, the signal is going to be degraded. Think of a tower like an umbrella. The panels on the tower are angled slightly, and the signal travels out in a straight line, and gradually drops. Like rain on an umbrella, it rolls down the slope until it falls off. If you are outside this drop (being higher than the tower) the signal strength drops, thus the signal loss. Sorry to detail it like that, but it is the only way I can describe how the signal falls on the plain as it is transmitted. The extender, I doubt Verizon will budge or lower the price. You might continue to call and see what they can do to help you. Not for sure if this helps, but hopefully it shines some light on the signal issue.
Sadly the extender also won't help a ton on an LTE enabled phone either. They only help with 3G service. What you'll need, until Verizon comes out with an LTE-enabled extender, which will require that eventual wireline Internet connection, is a Wilson/WeBoost repeating system. Those are sold with directional antennas that can likely get you an LTE connection if mounted in the right spot. It's unfortunate that trees and mountains are not wireless friendly. Especially pine trees. Those will totally kill your 1X and LTE reception (On 850Mhz and 700Mhz respectively).
Otherwise, hotspot should work on 3G if your phone's 3G data connection is able to provide the phone data.
Personally I would skip the extender all together. There are MANY free apps out there that allow you to make and receive phone calls over Wi-Fi, so if you have a strong and decent speed internet connection, I'd go that route.