But I actually think that none of these technicalities matter that much. What's missing in the EU democratic process is an EU wide platform for debate, a platform for campaigning on EU wide issues.
This is made more difficult by the fact that we speak so many different languages and that English proficiency is very unevenly distributed among the economic classes (and among countries).
I think what could spark EU wide political debates and allow campaigners to create real political pressure on an EU level would be a directly elected EU president. A face that you can properly hate and blame and really really want to kick out of office :)
I am very much in favour of the United States of Europe, modelled after the USA.
More theater, and a punchbag to sacrifice, like Bush was for Cheney. No thanks!
This is the fundamental problem with representative 'democracy' in general (at least with regard to legislatures); representatives aren't and inherently can't be held accountable for more than one thing per election cycle.
Of course you can vote out your MP, however there is a calculus at play: your MP might be great at the local issues, but then they may support a European rep that is not as good. It would be much better if the EU were directly accountable to the people upon whom they inflict their decrees.