Actually , my hypothetical presumed that the culture of government was already unified around my ideals.
In an alternative hypothetical, I could just rewrite all the laws and the constitution, and wait for these changes to permeate the government, and wait for the government to permeate other institutions. Admittedly, this process would take time, and the exact outcome would involve some evolution before it is completed, but rewriting the laws would effect culture to a large degree, unless there is a revolution halting the enactment of the new and improved legal system. The revolution would likely not come from what is generally thought of as culture though, it would more likely come from a subgroup of elite who would resist losing their power to the general culture.