Nic
answer to your query ("Is religion, particularly Islam, compatible with democracy?") is 'Yes' (my perspective while I'm NO expert on the faith issues). I'd give example of Turkey of Kemal Ataturk.
There are two facets of an Idea (or Ideology), One the idea itself and two, implementation of it. Many a times we blame the idea for the poor 'implementation'.
Moreover democracy itself is not the foolproof or 'the ultimate' governing tool. There have been other forms of governments in past, benevolent ones, and future may conceive some other, better, forms of government. This “process’ is eternal it seems.