Some of these scenarios sound like the high school question, debating the situation of a lifeboat containing “one too many” people to support — so who goes overboard?
Actual decisions are made to sacrifice human lives for the lives (or freedoms) of others all the time; it happens every time we take military action, for example. Ostensibly the lives lost in the invasion of Afghanistan are worth it to prevent the lives lost in future terrorist attacks on the US, that could have potentially been based in Afghanistan.
The point is, for a true supporter of the Mississippi initiative the 10,000 frozen embryos vs. 1 10 year old girl scenario SHOULDN'T be a puzzle; it should be an obvious choice to save the 10,000 "persons."
If you reject the scenario as artificial, consider this: in practical, real world terms, if we support the Mississippi initiative, we clearly should be devoting the SAME effort, manpower, and funding to protecting fertilized eggs and investigating and documenting their deaths, as we do to protecting little girls and investigating and documenting their deaths.