Recovery Mode: Backup options not showing
I was correct - the stock recovery was not being substituted for a custom recovery.

I have since tried a number of things:

First I tried installing the "FreeGee" app. Trying to install a custom recovery resulted in the error "Your devices specific software version of D80220d is not currently supported".

Second, I tried following this guide resulted in the error:

Loki tool v2.1
[-] Loki aboot version does not match device.
1|root@g2:/data/local/tmp # exit
1|shell@g2:/ $


What eventually worked was downloading the AutoRec .apk for the LG G2 D802 and installing it using adb:

adb install D802_AutoRec.apk

I downloaded the .apk from here. TWRP recovery was installed successfully. More information on AutoRec is here.