1) That sounds pretty damn good.
2) Having just lived for years in the south, I love me some cajun seasoning but I've got to say that sounds more like a substitute for andouille than a gyro.
To up the greek flavors a bit more maybe try-
Grate or thinly slice cucumber, then mix into the veganaise. Add cracked black pepper and/or dill and/or mint to taste. Let sit overnight. Gets you closer to tzatziki.
For eggplant, nix the cajun seasoning and sub a mix of greek spices. Your traditional mix will be lots of salt, some sweet and some hot paprika, pepper, parsley, garlic, and oregano. If you have any onhand you can also throw in to taste- marjoram, rosemary, thyme, and/or cumin. Sumac is also freaking amazingly tasty, if you've never had it (DISCLAIMER: the purple spice, not the poisonous plant, they're different things... and skip cumin if you're adding sumac).
I've always had gyros on pita with tzatziki, lettuce, tomato, raw sliced onions, and the gyro meat so I'd probably go for that combo if I was trying to replicate the flavor.