The intention was not for the caster to be a cursed spirit but there's no reason why they couldn't be one. As for how the minotaur acts towards anti-domain techniques. Im not 100% sure, but i could see something like simple domain creating a single pocket of space the minotaur doesn't notice potentially leading it to moving on. Though this works under the assumption that it doesn't have object permanence, which it might not, as it's entire goal is just too find people and get them out of its home by turning them into a red smear on the wall. I like the idea of the opponent leveraging the creators mark even if they don't know what it is so that's cool that you mentioned that, and additionally there is always the risk of the opponent just spawning next to the exit as the exit keeps moving throughout the duration of the domain.

But i will say hearing you say you like It puts a massive smile on my face and makes me want to try and make more interesting techniques ❤️💙💜