The egg would have to be Batul Beshishim, not the blood.
I didn’t learn through those Halachos, but to be Nosen Taam to what you describe we can say that once you had the Shaila on a whole egg and had to render it Traif, it is a Chaticha Asura and we aren’t Mattir Chad Betrei. On the other hand, when the Safek is born on the mix you can still ponder its Issur and add that to the Rov factor.