I've also come to accept that Western-style social liberal secularism is not the only legitimate path for people in the region to follow. When given the vote, at the very least, nominally Islamist parties such as AKP win (and this in a country considered more moderate than the Arab countries).
The AKP is not nominally "Islamist", but officially advocates for a "conservative democracy". The overzealous Turkish secularist institutions (the military and the constitutional court) banned previously the existing Islamist parties or ejected them from power, as it happened with Erbakan. Of course, the AKP is rooted in said parties and it could be defined as "moderate Islamist" or "Muslim-democrat" (something like a vague equivalent of the Christian Democracy), but Erdogan would reject such characterisations. Actually, Turkey and the AKP have had a singular evolution. Perhaps this article might help to understand it:
http://www.brookings.edu/research/papers/2012/04/24-turkey-new-model-taspinarAs for the first part of the paragraph, I tend to agree. I think we cannot expect that other countries are going to trace our model with carbon paper. Perhaps it'd be more realistic trying to export some basic concepts on democracy and human rights, in order that other countries will adapt them to their realities, cultural contexts, systems of beliefs, etcetera. In any case, such processes are slow and gradual, with ups and downs (see "Arab Spring").