The bills would even limit the Education Department's ability to offer states incentives to adopt strategies that have proved effective - as the Obama administration's Race to the Top program has done.
The sentence is not ambiguous at all. This is the reading of /has done/: as the Obama administration's Race to the Top program [has limited the Education Department's ability to offer states incentives to adopt strategies that have proved effective].
/Has done/ refers back to the WHOLE part of the sentence in bold.
Allow me to write a simpler one:
The man's behavior has proven disastrous for the school as John's has done.
Rewrite for comprehension:
The man's behavior has proven disastrous for the school as John's behavior has proven disastrous for the country.
Here's the TRICK: everything that comes BEFORE /as/ also applies to the entire clause that comes after as. It is a mechanism for avoiding repeating the whole thing.
The bills would even limit the Education Department's ability to offer states incentives to adopt strategies that have proved effective - as the Obama administration's Race to the Top program has limited the Education's Department ability to offer states incentives to adopt strategies that have proved effective.