No Service/searching after cracking screen: Antenna Replacement?

Hi all.

I recently dropped my ever so fragile iphone was dropped and cracked. The crack isn't so bad but a small chunk of glass is missing from the top left hand corner around the antenna.

The real problem began when my phone started saying "searching" for service. I tried everything on ever forum that would have fixed a software issue (reboots, restoring, settings ect.) which makes it clear that its a hardware problem. Apple store wasn't fully useless, the employee said all he could offer was "warranty repair" which costs as much as a warranty phone and they basically just send you a new one.

I would like to explore my cheaper options first. I'm an electrical engineer so while I don't have much phone experience I know how to solder and am quick to learn with some direction.

Will replacing the cellular antenna fix my problems? Has anyone done this repair and can grace me with their experiences?

Thanks in advance, I appreciate any direction if you know more than I do.