Long bump, but I have managed to resolve this issue for anyone else who might have a similar issue.
The problem was entirely with the phone, and may or may not exist with other phones. If it does exist with yours, check the below, and follow instructions to fix.
The issue lied with the GPS radio in the phone being partially broken for some phones, an unknown reason, and Google wasn't set out to fix it with ease. In Android versions 4.4.3 and 4.4.4 KitKat release, the GPS, and some other radio firmware are partially broken, and cannot work properly. If you have issues with your GPS, check your Android version, and if it is 4.4.3 or 4.4.4 follow below for a fix.
To fix, you need to install the older radios from 4.4.2 onto the phone, overwriting the ones from 4.4.3/4.4.4. This can be done through the XDA Developer forums, which will often have good walkthroughs, but it will require you to enable USB debugging on the phone, installing the correct drivers, and using ADB (a command line program for flashing and controlling Android devices) to make it work.
I fixed my issue by upgrading the phone to the Android L Developer Preview, which is unstable software, but seems to be doing me fine so far. I am experienced enough to be able to fix any issues that may arise, and it's not recommended for an everyday essential phone. I now can find ~20 satellites and fix a position from around 6-14 of them when in the car, and everything works perfectly.
~ZionGo to the full post