If I had to throw my hat into the ring, I'd say, reluctantly, that Six should stay a friend. Part of that is narrative cowardice, I don't want Yrs to be stuck writing the Husbando Wars into every interaction.
But even in character, I don't think Six and Qi dating is best. I'll admit I love the idea, it's really cute, Six can really bring out Qi's fun side.
But Six and Qi have never really interacted as would-be lovers, and theirs already imbalance in any relationship they build. Qi admitted that she's never looked into Six as deeply as they looked into her. That's a place for toxic stuff to fester, and forcibly introducing that kind of emotional vulnerability not just into Qi's relationship with Six, but her relationship with the potential Husbandos seems liable to make it worse.
After all, someone has to win the Husbando Wars, which means others lose. Bringing Six into this when Six has so much narrative momentum and baggage really leaves me worried about either the Husbandos having to compete against Six, or having to figure out how comfortable they are with throuples. Edit; That seems a little cruel to them, to play with hearts is no laughing matter.