One possible AU headcanons about ByaTomo:
The Kuchiki elders arranged behind Byakuya's back his engagement with Tomoyo, because they finally got tired of the fact Byakuya was basically avoiding his duties as the Kuchiki clan's head.
Byakuya wasn't at all happy about this. In fact, he had decided to do everything in his power to make Tomoyo dislike him and call off the engagement as she had the power to do so. The engagement had been made between her big sister (who is the Empress) and the Kuchiki elders, yet because Tomoyo's big sister cherishes her little sister and since Nihon (the world where Tomoyo is originally from) didn't technically need this deal if Tomoyo would just say the word, the engagement would be canceled.
Too bad Tomoyo had other plans. Now that she finally had the chance to explore the world, she would do so...even if Byakuya would suffer slightly from this. After all, the deal was as followed: Tomoyo would spend few months at Soul Society to get to know her future husband before it would be decided if she and Byakuya would indeed get married or not.
Eventually, things would escalate into that, they both would have a big show-off between each other. It would be enough to cut the tension between them and make them realize there might be blossoming feelings between them...