Well, maybe Russian women like being pictured as someone's possession... Or maybe they are dating sailors.... En i varje hamn, det vet de om...
I have still a question what phrase is correct:
Du är min bästa kvinna
Du är min bästa kvinnan?
Concerning this verse, I would like to explain that this verse is about one women who was in the past with the author, but later she decided to choice another man as a husband. It was many years ago. But the author still remember her and has expressed his sence in the verse.
Taking into account your message, I conclude, that "kvinnan" is better than "kvinna".
Concerning possessive and creepy... I do not think that possessive, but agree that this verse is very sad. When I wrote it, I remember Minnet by Dan Andersson.