the lack of democracy in the EU is my main reason to oppose my country joining the EU.
Not that I hope your country joining, but could you please elaborate on that?
Council of the European Union is the place where you send YOUR chosen leader. Vote for party or person, gets to be prime minister, leads your country, represents it internationally. Nothing undemocratic in that.
Each member country has a representative in the European Commission. National parliaments or goverments propose the candidates. Each member has been selected of the candidates of each country, and have been accepted by national governments or parliaments. Nothing undemocratic in that.
Then there's the European Parliament. With its >750 members each country has representatives there forming alliances and voting blocks with other members. It's the biggest parliament in Europe, decades ago it was though to be a mere discussion forum but EP has gained some real power in EU especially after the Lissabon Treaty.
I am certain we could have more democracy within EU. One part of that would be to give more power to directly elected organs like EP as traditionally especially the Council and to some extent even the Commission have been about promomoting national interests.
That would necessarily mean giving more power to the European Parliament, and less to the organs which traditionally have been the battlegrounds for national interests like the Council.
Many people who opionate that EU should have more democracy also opionate that countries should have more sovereignity (as if they didn't have that already). Usually they do not further elaborate on that as that would be revealing: their two goals are opposite of each other. You cannot have more democracy in EU without giving more power to the democratic organs of the EU.
Personally I'm all set for it. I do hope to see more power transferred to the European Parliament, but I realize it's a slow process.