DT is a general super form kind of thing, how to put it, it does indeed make your styles stronger because generally you just became stronger, so more accurately, your Huntress style becomes faster, and Beasthood style becomes stronger during DT, it's already assumed you can switch between the two styles on the fly, so you don't really need to have both styles gain the traits of the other, because you can use both fairly freely.

As for Vileblood... Actually, why not make that your Devil Trigger? You take a somewhat demonic form, heightened defenses and such, but can still use your weapon. That said, seeing as your character is still largely human, your form actually won't change very much, you'll still look quite human, maybe with glowing eyes and growing some scales or fur depending on the attribute of your demonic powers.

Otherwise Flip-Off looks fine, and so does Demon's Omen and Chomp!