As I recall from my days as a short order breakfast cook, when we could get them, we would by duck eggs for use in the daily breakfast special. Yes, different species of egg taste different. The difference between duck and chicken is subtle yet distinct and seemed to be largely covered up if used in an dish with other ingredients such as an omelette.
Goose, I’ve only had a couple of and don’t really remember much about except they were green huge and double yolked. The rest you mentioned, I dunno.
We collect our goose’s eggs so that she doesn’t incubate them (a pair of geese is two too many). I usually scramble them for the dogs, but occasionally my gf requests one over-easy. (shut up)
It’s not easy to cook a goose egg to perfect over-easy, but with basting all things become possible.
The color doesn’t matter to me. I’ll admit that I’d suggest not getting white eggs if you can avoid it, for the reasons you mentioned, but that’s it. I have no issue with white eggs, but they are indeed associated with store-bought.
I think the novelty of different colored eggs like you describe would actually let you charge more, to tell the truth.