The air is already displacing out ahead of the car as if it had some phantom nose. It's referred to as a Prandtl line of discontinuity.
In the Volkswagen photo link you can see this.
You need an uninterrupted pathway for these streamlines to get over the leading edge of the hood.
A splitter would look like a 'wall' to the air, with the potential to create remarkable separation and turbulence.
The air 'knows' what to do.
I recommend that you abort any attempt to direct it sideways, and just let it go where it's gonna go. That raked-back radius on top of the nose ought to be enough for attached flow.
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