Reboot
Base it much more heavily on the classic horror movie homage the original Castlevania was founded on. Maybe give it an old film style presentation and feel, which they've already played around with like the faux film reel effect in Castlevania 3, and sort of like what The House of the Dead games do.
3D action is fine, but it should be designed in a way that makes it slow and very methodical in its pacing like the original, as opposed to typical modern character action games like God of War or Bayonetta. I think slowing games down on purpose has a value that is getting more and more underappreciated. Progression-wise, I'd be fine with something inbetween Dark Souls and the Metroidvanias. Maybe even take some cues directly from classic survival horror.
Soundtrack should be Mellotron-infused Italian schlock horror rock in the vein of Goblin. Anima Morte is a good modern example, and doesn't really stray too far from established Castlevania music either.