Alright, I like a challenge...
Let's say... the ancestors wanted to look out for their descendents, so a lot of them put an impression of their soul into various items that were passed on to their children. Similar to how paintings work, but without your ancestors complaining about how things were different back in the day.
Ginny's soul was in flux after being partially eaten by Tom in Chamber of Secrets. This led to her soul being a bit more flexible for a few months after, parts of it breaking off and coming back as it tries to find its equilibrium. Part of it attached to the butter dish impression, taking a bit of the impression back to Ginny, while leaving a part of her in the dish. Eventually a more solid bond formed between the butter dish and Ginny, and part of her soul acted as fuel for the impression, making it more real and aware than it otherwise would have been. So we have a soul bonded Ginny attached to a butter dish. Many a fic has had a relationship be amazing just because of this bond, and struggling to overcome the prejudice of society towards their unique love sound about right.
Fanon says Weasleys know a lot about fertility magic, so let's use that. The butter dish has the soul of a Weasley who knew more than most about fertility charms, and working with Ginny, they manage to figure out a way for magic to use his soul as material to achieve conception, rather than the traditional bodily fluid.
Ginny reveals the truth to Harry after finally getting the spells to transfer her lover into a more suitable vessel, so they can truly be together.
I could probably keep going. Somehow I'm warming to this story plot idea...