Low voter turnout is only of concern to mass appeal parties, who have to get the voters out. Small, racist, xenophobic or skeptic parties actually favour apathy because it is populism's best friend - you only need your buddies to turn up to send off your leader to his super job at the European Parliament.
I would recommend single country constituencies with complete proportional representation and a 5% Europe-wide vote threshold; make the Commission the proper executive branch; and turn the current Council of Ministers into a Senate (4 senators from each country would do nicely).
What is, after all, the point of a couple of Polish League of Families members sitting in Strasbourg / Luxembourg / Brussels, apart from being a token conservative Catholic presence? They represent Vatican City more effectively than Poland since their policies are more relevant to the Pontiff's family than to modern day family life in the rest of Europe.