Regarding the minimally unethical are you sure about that?

Like do you know what happens to the male born chicks? Or what happens to the hens that stop giving eggs? Or in what conditions do they live? And about dairy, do you know what happens to male born calves? And what happens with the cow when she stops producing milk? And how the cow feels when their children are taken from her?

My friend, eggs and dairy are even more brutal that meat industry, which they are the same industry by the way.

It's very difficult to consume dairy without animals being killed, because cows need to be pregnant to produce milk, which has the side-effect of more cows. In industrial production, we're talking roundabout 5 calves over the lifetime of 1 milk cow. Those calves are not being kept around.
You'd need to find a farmer that only milks their cows when they get pregnant naturally.

With eggs, backyard chickens can be argued to be moral (given humane conditions). But industrial production involves male chicks being shredded and horrendous conditions for those that get to live.

In either case, I'd consider a vegan diet with supplements so much easier.