I agree there is a strong democratic deficit in the current EU governance structure, but I disagree with a proposal such as

> directly elect some kind of president

We do not need a president with over-powers, and electing directly one does not solve anything for democracy, as the recent history in countries like the US and France shows. The point of directly electing a president is giving that role more power. The current structure in the EU is not so much president-centric either executive or legislative wise, but more like comission-centric, which is what imo has the biggest problem in terms of democracy in the EU.