Jean-Claude Juncker was voted in by the European Parliament who are in turn made up of the MEPs that you are eligible to vote for. He has a term for 5 years and then goes. He was voted in Nov 2014. Arguably more democratic than the positioning of Cameron (whose leadership of the tories was a private ballot) and who i have never voted for and yet is making decisions for me.
In fact people who want him out but live in areas that have high tory support, or even his own constituency, will never get the chance, so much for British democracy. You cannot dethrone Cameron.
van Rompuy is the ex leader of the European Council, now run by Donald Tusk. The council is separate from the EU. He had his own advisors or in British terms a cabinet. His position is also rotated hence Donald Tusk now doing the job. He was voted in by the European council who were the heads of state. Again, those heads of state are voted for by you.
So, as the democratic principle is of paramount importance to you, you can rest easy knowing that your vote is in there, somewhere, just like everyone elses, including those that have different views from you, but the principle stands.
To vote Remain is the democratic right of anyone, to call it indefensible is to argue against democracy.