Hermione goes forward with the ritual with one slight caveat.

Hermione had made her way in front of the Veil and was enraptured by the sounds emanating from behind the curtain. She was drawn to the voices and had to keep a firm control on her thoughts to not become swayed by the allure of the Veil.

Taking out the Invisibility Cloak, she carefully set it down in front of her as she kneeled on the stone slab facing the Veil. She then took out a several vials of blood replenishing potions and a silver knife and placed them all next to the Cloak. Using the knife, Hermione carved the rune for death into the stone floor in front of the Veil and then grabbing the Elder Wand tightly in her grip— then cast a diffindo onto her forearm, and winced as she saw the blood trickle from her arm, onto the rune...

...then whispered ‘invoco mortem.’

As the Veil’s curtain started to move and shudder against the archway, she centered her magical core and utilizing her inheritance, was able to feel the essence of her soul and that of her Father’s, which had bound itself to her magical core in the form of his horcrux.

If this was going to work, she needed to separate his essence from hers—protecting her soul and binding his to Death.

Casting the Romanian spell silently over the rune of death, she saw it glow in a blinding white light—her blood was freely flowing at this point and she was struggling to keep the spell focused.

Once the glow peaked and the room was bathed in a blinding white light, causing the ground to shake, she used what was left of her magical energy and yelled in anguish, “Teneat libere mortem filio domini Sic fiat Gaunt!”

(Master of Death bind to the son of Gaunt given freely, so mote it be)

At that exact moment, the Veil flashed in a blinding haze of pure light that rivaled the brightness of the sun and with all her remaining magical energy, she pulled her soul inward and collapsed completely onto the ground.

Her final conscious thought was hoping that she hadn’t just made a gross miscalculation where her Father was concerned.