I don't see how adding a nonce helps. If I can find two "random" strings with the same hash, I can surely also find two random strings which both begin the same nonce which also have the same hash. You're not reducing the search space by specifying that both strings must have the same prefix.
Collision attacks are much less expensive than hash cracking. Crafting during months two unconstrained seeds with equal hash is more feasible than making them both fit a nonce that is changing every 10 minutes or so.
However, I concede that neither case is provably fair once collisions are possible. It is only about strengthening the system with collisions.