Two things wrong with this. First, the conservation of angular momentum says that you cannot change the orbit of any of the planets without affecting the system as a whole. It does not address the direction of the orbits or the rotational direction of any individual planet. This is why the notion of Venus or Earth ping-ponging around the Solar System is so wrong.
Secondly, the Big Bang has nothing to do with the rotation of the Solar System -- the latter was set by the spin of the accretion disk from which the Solar System sprang, and that was determined from the supernova-enriched nebula from which the accretion disk formed.
Oh, and by the way, before you claim that no one has ever seen a solar system forming from an accretion disk, please do a little research.
Never tested the theory have you. It doesn't speak to orbit of planetary bodys, it's a general principal. line the inside of a centrifuge with spheres and cap it. Spin it up, pull the top and note the action of the spheres, they launch out spinning in the same angular motion as the centrifuge. That is the conservation - whatever is launched out carries the same angular direction as what launched it. In a frictionless environment, this will be unaffected and unchanged over time.
In the case of encountering friction, the spin should come to a halt. That is your problem. You have retrograde moons, planets, galaxies, etc. Gotta account for that somehow or the big bang is nothing but a big dud. And you guys know that.