I've managed to figure it out. It seems that the main issue was that GRUB hadn't completely installed.
First, I used the elementary OS live-boot USB that I'd made with Rufus to boot into a live environment. I needed to install boot-repair, which needed a repository added. I ran:
sudo apt-get install software-properties-common
Which allowed me to run:
sudo add-apt-repository ppa:yannubuntu/boot-repair && sudo apt-get update
sudo apt-get install -y boot-repair && boot-repair
I followed all instructions, made sure to ensure that GRUB was purged, and after reboot, the laptop booted up perfectly!
However, after the first reboot, the problem returned with an additional error message:
Failed to open \EFI\BOOT\grubx64.efi - Not Found
Failed to load image \EFI\BOOT\grubx64.efi: Not Found
start_image() returned Not Found
So I booted back into the USB live environment, opened a terminal, and ran
sudo cp -p ubuntu/grubx64.efi Boot
sudo touch ubuntu/grubx64.efi.gbr
Now the laptop has no issues when booting. :D