There is inevitably going to be some wild yeast or bacteria that has found it's way into your wort. No matter how sanitary you have been.
The whole key to sanitation, quick chilling, and proper pitch rates is to increase the potential for the yeast to take over the unfriendlies and create an environment they don't like. Examples; CO2 and Alcohol.
You might be okay to freeze the wort but I doubt a carboy would survive those rigors. And even if you did freeze the wort, I'd suggest you bring it to a boil and re-chill before you pitch any yeast.
Good luck with that.
What I really don't understand is why the staggered additions?
Are you extract or AG?
If extract, why not just add a late extract addition to increase the OG?
If AG, why not parti-gyle?