Fix Broken Launcher on Soft-Bricked Device
Solved my own question, thanks for the help.

To get into recovery mode on my Moto G2, I first went into the bootloader by force shutting down the bootlooping device (hold power until it turns off) and then pressing Power and Volume Down at the same time for 2-5 seconds. I then selected 'Recovery', which came up with the boot animation and then a dead android with the words 'No Command' written above. I then pressed Power for 5-6 seconds and tapped the Volume Down button, which took me to the recovery mode menu.

I then selected the option 'Wipe data/factory reset' and selected 'Userdata only'. Once it wiped that, I rebooted and waited ~10mins at the booting animation before it took me through the Android setup wizard. All of my data was restored through Google Drive and Google Photos, even stuff like the order in which apps were displayed on my homescreen.