"My very good sweetheart cooks for me."
..was my attempt. I suppose I should have seen that "koramiko" was clearly masculine.
That was a good guess, because the word amiko is, on its own, gender-neutral; you can use it for a male or female friend. It just so happens that koramiko and koramikino are conventionalized terms for 'boyfriend' and 'girlfriend', respectively. This isn't predictable given the meanings of kor- and amik- as roots, but it's just how things happened to turn out as people used the language and terms started to stick.
"Sweetheart" is most used like an adjective, isn't? So, there is a substantive in this sentence. Although they're synonyms.
When I think of the word sweetheart, I first think of it as a noun. It can be used as an adjective, but I think its most common usage is as a noun.