I hear you both but this statement has me wondering. I agree that you have 100% control over who you involve yourself with. By saying this, do you mean to indicate that Amy is only allowed to date someone that you are interested in involving yourself with? Do you not see yourself having the option to choose to not involve yourself with someone she is seeing?Otherwise I will choose for my self to have some level of discretion over my metas because despite popular belief here, they are my metas too and I have right of consent over who I involve myself with.
Are you both are intentionally only seeking a relationship structure where there are healthy relationships between all metas? If that is the case it still does not make sense that you would limit the dating pool along such a narrow line as how someone openly labels themself. I am not advocating looking for a needle in a haystack but I am also advocating for not building a fort around the haystack.
I like to think of this like boundaries v. limits. We have boundaries for our relationship for things that impact us both. I look at limits as something that is 100% for my partner to decide. From what I have seen, attempting to set limits for your partner is what crosses the controlling line. Your situation in this light might look like Amy can date whomever she wishes. If she finds a partner that she wants to take the relationship to a different level then it should be someone you are comfortable with as a meta. If you have a relationship boundary that you only want to have metas that you can and want to engage with, ok. Why not trust each other to vet their own partners based on that criteria rather than draw a line in the sand on how they choose to identify? Do you really think Amy wants to engage with a truly mono partner that's going to subject her to mono ideals?
Good luck! I hope you both find the happiness you seek.