I'm glad I found this thread and read through it. This is a much better place for me to post bomb than in the comments section.
I feel like Rei and Hina's relationship has taken a new turn. I mentioned this in the comment section but I'll restate it for new readers: chapter 52 saw a change in how Rei views Hina. Her line about not regretting her choice, even if it means she'll end up alone, because she did nothing wrong effected Rei strongly emotionally. In a sense, with that line Hina showed Rei a new "route", one that lead him away from viewing himself as the cuccoo bird that has caused the Kouda family to suffer, to understanding that even though he has ended up isolated and alone he still has done nothing wrong. This revelation has caused Rei to feel like he owes Hina a debt, which would later lead into him trying to find a way to stop her bullying.
But, at the same time, I think it's a bit more subtle than that. There's the lines where Rei thinks, "I felt the urge to immediately hunt down every person who made her cry and tear them all to pieces, but ... 'That won't fix anything.' 'That won't do a thing to help her.' So...Think. Think. What should I do?" Look at the progression of these thoughts: First, Hina cries and his first, instinctual reaction is to find the people who made her cry and "tear them all to pieces", this violent urge is very different from anything we've ever seen from Rei and seemingly has nothing to do with the debt. It's only after that, when that subconscious, instinctual urge fades, he tries to think of other ways to help her because of the debt.
I do not necessarily think that these subconscious feelings are romantic in nature, at least not yet. However, I do think it's important to note that when Rei talks to his sensei about Hina he lists her personality, good looks and admits to the fact that she's important to him, while only after explaining that that he owes her a debt. So he has these feelings for her, which I believe are those of a older brother for a younger sister at the moment, and he's using the excuse of him owing her a debt to rationalize the decision to act out on those feelings to help Hina.
I look forward to seeing how Rei responds to this "epiphany" in the future - especially in regards to his loving/hating shogi and his family dynamics.