The AV Buddha looks quite funny, that was the original reason why I began to think of alternate religion videos.
The idea for them would be, that they'd show something of a religious ritual, like in vanilla civ. For the Octopus Overlords, that would be something like this:
[hollow-sounding drums, in the background]
[whispers of zealot names ('the great one has watchful eyes', 'those in the deep will never sleep', 'i can do ventriloquism lol', 'beware the might of the overlords', etc.) repeated all the time, in the background]
-The black begins to withdraw here, showing a OO-mana node-like structure inside a temple, with those slimy green-grey chains. (I love those chains

)
Between them a dreamer is chained[?] in place, with all those burning wax needles and all-
[about here strings, a bit like in the opening slideshow but higher-pitched and faster, but not too dominant (I think the slightly techno-like Desert Rose, while sounding good, is slightly out of character for medieval fantasy, so I'd use older instruments but a similar melody could work perfectly)]
(the camera zooms slowly over the ritual)
[here, singer comes along, singing some gibberish from the overlords (no, no inspiration taken from the Desert Rose at all

)]
-behind the dreamer, there is a cultist standing in front of the squid picture-
[end the singing to a couple of seconds instrumental only, then something that would sound like what the overlords say through the dreamer, in a suitably weird voice, volume lowering gradually to silence]
(the ending screen is a large picture of that OO squid, the religion symbol)