What is needed, as I have argued before, is a bottom up exercise which explicitly excludes the national governments and parliaments (at least as much as is constitutionally practicable).

I still favour a constitutional convention, comprised entirely of people popularly elected for the specific purpose of writing a constitution beginning "We the people". The text, if one emerges, should go to a simultaneous referendum in every member state and if approved (say) by a majority overall and a majority in two thirds of the member states should then come into force for those members that have so ratified. Any states which reject the constitution would then continue with the existing arrangements (not an ideal solution but it ought to be manageable at least for a few years).