31 Heavenly Dragons' Power in Vampire+Rosario

Yes, I know I use Highschool DxD too much, I can't help it, it's a really easy series to make fan-fiction for. But in my defense, this one is taking place in a different world, I'm just using the Boosted Gear and Divine Dividing for the protagonist. Obviously, the MC will have to be Human, considering only they can have Sacred Gears. Well, you could have him eventually become a Dragon, through the two Sacred Gear's powers, but probably do that only after having him get the Human Modification procedure from Tohou Fuhai, later in the story. These are just suggestions for possible future plot points.

So, onto a big plothole: How can he have both Boosted Gear and Divine Dividing? They're opposite powers, the rejection would kill him. Well, I'll say that maybe the rejection is killing him, use of the Gears causes him immense pain which grows when the two Dragons start to bicker. Maybe by the time he reaches the Academy, he only has a few years left. That would make the story have a sense of urgency, the short time being used to find ways prolong his life. Of course, that is only if you want to use that plot device.

The beginning will either be a transmigration or a reincarnation. The MC will either originally be from the DxD universe and somehow made his way to Rosario+Vampire or he died in his old world and was reincarnated in the new world with both the Boosted Gear and Divine Dividing.