Default [Q] Signal issues.

I've had my G3 since last week and I'm starting to get very frustrated with it. I have absolutely no issue with the phone itself. Its snappy, screen is beautiful. UI is fine, and honestly I don't even feel the need to root (yet)

My problem is the LTE on the phone. I have my phone USB tethered to my PC in a window to give me high speed. We only get dial up where we live and LTE is the only source of highspeed available. Frustratingly during the day between around 11am and 8pm Its like pulling teeth to get the phone to stick to LTE, every 1-5 minutes it switches down to 3G and stays there until I put it into airplane mode and back. Then LTE pops on again and its fine for another 1-5 minutes. During the night it will stay for hours. I've even taken off the back case to somehow eek out a little more signal strength.

Now I know that this could be a provider coverage issue, but my mother's Galaxy S4 stays on LTE even during the daytime and has one more bar of signal.
So before I throw the phone across the room in frustration, I was wondering if anyone knows of a way to change the LTE/CMDA settings beyond the crappy preference options (that doesn't work) in the mobile data settings. I can access the hidden menus but I don't know what any of it means. Is there a way to force LTE on permanently, or disable 3G data. Are there any nice network diagnostic tools to track signal strength as I move the phone to different areas, or compare it with other phones?

I love this phone but if I can't find a fix I may have to replace it with another device.

TL;DR: Need help getting LTE to stay on, settings or tool recommendations welcome.