I agree that it isn't compatible. I'm deeply troubled that you're against democracy. It's the most stable, proven system of government. Islam mandates a dictatorship and we all know how those end up. In Ghadafi and Sadam's brutal, decades-long rule, the US had 9 presidents. Say what you will about them but the US population changed governments 9 times during Ghaddafi's reign, and expressed their resentment at the ballot box all those times, something people in Libya and Iraq were deprived of.
This has massive conseqences because resentment built up against Ghaddafi and Saddam and there was no lawful outlet for people to express that for decades, which paves the way for what's happening today. I'm not saying they were very Islamic but I'm describing what happens with dictatorships.