On 'Europeanising' parliament elections in the public's mind, I can think of two things: (1) have the EP parties run directly, rather than through their local branches; (2) make the Commission truly EP-elected, which would focus voterss' minds. Of course, the 'Eurosceptics' would oppose the latter change tooth-and-nails.

On the Bundesrat: it is followed by the press, much more so than the EU Council, because they can block legislation passed by the elected lower chamber (the Bundestag), and negotiate a modified version (which IIRC then needs Bundestag approval again in each case). The federal-local entanglement is more complex than we can expect for the EU in the near future: it's not only that there are regional expectations on a state PM to deliver something, but state PMs also play party politics, and regional elections are often influenced by the mood on federal politics. Even if I don't think most voters consciously vote for changing the Bundesrat composition, there's the intent to change federal politics and it can bear results.

_{*Lunatic*, n.
One whose delusions are out of fashion.}