Why not just implement Companion Glamour akin to Egi Glamour? All that would be required (besides adjustments) is a new skin. Imagine if any of your mounts could be your Companion.

Of course, some would look absurd doing certain actions so many have to be excluded or be only a certain 'type', for example the Dandelion mount from the Moogle quest would be more suited to healing & a Magitek mount better as defensive.