There are a ton of posts to sift through so forgive me if I have overlooked something.
From what I can tell this user does not have access to a landline internet connection (coax,dsl,fiber). He uses satellite for his TV at the moment and there may be a local Muni WiFi service provider in his area willing to broadcast a WiFi broadband signal to him, but that is unconfirmed.
That means all Verizon Network Extenders are out of the equation. NEs are only going to help if there is a reliable broadband connection behind them providing a consistent connection. Satellite and Muni WiFi isn't going to cut it in my experience.
That leaves him with the a 4G router that talks directly to his local tower(s?). The best thing he can do is boost his reception with a booser/amplifier kit. I cant tell if he already purchased one or not but it sounds like he has and also worked with a local tech at some point or another (for the GPS concern?).
Roof mounting the GPS antenna should not be necessary. Satellites would be just as visible a window facing the equator with a clean line of sight as they would on the roof, although roofs will certainly perform better. Having to mount a GPS antenna on the roof suggests the area is covered heavily by trees or other objects that are otherwise not present on the roof. Users need a minimum of 4-5 good GPS satellites to get a lock. There is not much of an advantage of viewing more than the minimum with these devices as they are stationary. Once locked the GPS coordinates are not very important anymore. GPS performance is not related to the throughput of the device itself.
So... If this were me I would spend my time playing with the booster kit to get the best VZW service that I could in this environment. Sounds like he already has a roof mounted antenna to play with so I'd consider adding that to the solution to improve the results. If the native signals in the area are too poor to begin with then the booster isn't going to make much of a difference and alternative service providers or setups should be considered. Generally speaking placing the antenna higher in the air in addition to a higher powered antenna/booster kit will improve the results.
