Secession is the only real hope. Maintain the free trade and common labor market, but get rid of the Euro and leave the political sphere. Losing your sovereignty to a national government is bad, but getting it lost to a multi-national government is even worse.
It doesn't promote anarchy per se; it's a bit more complex. In Liberalism, Mises himself wrote: We call the social apparatus of compulsion and coercion that induces people to abide by the rules of life in society, the state; the rules according to which the state proceeds, law; and the organs...