Moreover, countries can leave at any time, as the UK has just done. All round, seems to exceed your criteria.
Your "Moreover, countries can leave at any time, as the UK has just done." sounds a bit odd in the context of this argument. "It's silly for countries to leave the EU on the grounds that it's not democratic, when it's obviously democratic because countries can leave the EU".
Yes, technically correct. What happened last time however was that the EP said "We want Juncker and we'll veto anyone else". There was a long staring contest and the EP eventually won. A veto isn't a technicality that you can approximate away - it's just as important as being able to propose laws.
The national leaders generally didn't like this, because they prefer the EU being more like a (huge, weird) deal negotiation table than something with direct representation. The national leaders are ultimately in charge, so this whole episode is mostly an unforeseen consequence of past treaties that they're willing to tolerate.
But hey look at EU over there
Well, you could try voting for national politicians and EP fractions that doesn't like the person in question. It's unlikely to succeed, for much the same reason that voting to get rid of national politicians is unlikely to succeed, but that's more of a tyranny of the majority kind of thing.
"If one meets a powerful person--Rupert Murdoch, perhaps, or Joe Stalin or Hitler--one can ask five questions: what power do you have; where did you get it; in whose interests do you exercise it; to whom are you accountable; and, how can we get rid of you? Anyone who cannot answer the last of those questions does not live in a democratic system."