Deploy the distracting lore dump!
This is becoming “I want to romance Akari: the thread.” So let’s move on.
I’m hoping that if i lay out my plans for the overall plot here, that you’ll see why romancing Akari is impossible.
This will obviously contain spoilers. So only open if you want to know. And please spoiler tag any replies, or I’ll be very unhappy. 
Rough plot outline.
Act one: Backstory selection and the mission to kill Kaito. Introduces Makoto and Kit.
Act two: Introduces Masa. This is followed by a mission to find an imformant taking part in a deal below a live concert. The informant turns out to be Ryoji/Ryuko. The comnotion below the stage attracts the attention of Midori, and she runs away from her producers to follow you.
Act three: The casino job. Ryoji/Ryuko informs you of the Busujima’s private, high-end casino, which is also Akari’s base of operations, that they only allow entry to people who have a special card. Upon acquiring said card, you infiltrate the casino and manage to take down Akari.
Act four: With the success of the casino job still lingering, the group enjoys some downtime. You, on the other hand, try to convince them that you need to act, Izanami-No-Mikoto’s warning of a deadline still fresh in your memory.
Act five: Having managed to convince everyone, you assualt the Busujima’s main vault, running away with millions of Yen. This draws the attention of Tsukasa, and a high-speed car chase through downtown Osaka ensues. The chase ends with Tsukasa either being arrested or killed, depending on choices. (As for why this choice wasn’t available for Kaito and Akari, all i have is three words. MC character development.)
Quick prelude before we jump into Act Six. By this point, the MC is going borderline insane from repeated violent deaths and is starting to not notice pain. On the other side of the battle, Toshiko is also going insane from trying to convince the rest of the family to stop ignoring the threat of “the Onryō.” Shakunetsu’s health is also getting worse, and by this point, he is practically bedridden, so Toshiko is essentially running the family by herself. The pressure on her is building, and she is a stone’s toss from a breakdown. I’ll talk more about Toshiko later.
Act six: Toshiko corners the MC and forces them to learn an unfortunate truth. As for what that truth is, are you sure you want to know?
Act seven: With the group having been torn about by the previous revelation, you set about hunting down Toshiko alone. When you finally find her, you come across a horrifying scene. She has murdered her father after suffering a breakdown and then killed herself.
Act eight: Toshiko arrives in Yomi as an Onryō, and accuses Izanami-No-Mikoto of being the cause of her family’s destruction due to her having sent you back. Izanami-No-Mikoto ends up sending Toshiko back to life in much the same manner as you.
Having thought the fight was over, you set about reuniting everyone and enjoying whatever time you have left. But you are surprised when Toshiko appears out of nowhere and kills you. You rewind many times but always end up losing to her. You eventually learn, however, that Toshiko has gained the same powers as you and that you have, in fact, already beaten her multiple times, but she always rewound, so you forgot about it.
Act nine: Seemingly locked in an eternal battle, you and Toshiko fight it out for eternities. Until the two of you manage to kill each other at the exact same time, and something strange happens.
This time, upon rewinding, you experience a bright light. You look up and see a woman’s face staring down at you. A man then pushes his head into your view, and after the two of them talk to each other, you realise that they are Hayumi and Shakunetsu Busujima. You look to your left and see baby Kaito before you realise that you are now inside Toshiko’s body and have rewinded all the way back to her birth.
Now forced to experience Toshiko’s entire life, you wait 31 years to return to the final battle from her perspective, but it is just before then that you end up in Yomi once more. Izanami-No-Mikoto admits she has made a mistake, one which she intends to fix. Having accidentally caused a time loop, she gives you free reign to move through Toshiko’s entire life and change whatever you see fit, as long as you fix the time loop.
Meanwhile, Toshiko is living through your life in the same manner.
Act ten: the epilogue, which will be entirely dependent on your choices from other acts.
Finally, the note on Akari. Trust me, I’ve tried, but there is no way I can fit a romance route for her into this story. There may be a way for Toshiko to be romanced, though, but I’ll have to think some more on it.
Have a great day, and remember your spoiler tags!