You wrote: "...The reminder is the Quran so remembering the Quran is reminding yourself of Allah. ..."
This is the confusion you are creating my brother. Remembering God need not be via Quran alone (though for Muslims it often includes Quran), you can do so even without Quran. For example, when someone remembers God even without Quran, he/she is reminding him/herself of God. When someone makes a Dua/supplication, it need not be the words of Quran, like prophet Zachariya is doing in his prayer/salat. The end goal is Man remembers God under all circumstances, this is meant by the phrase "the remembrance of God is great". Obviously you would want to know the commands and injunctions of God to be followed in various situations, thus, knowing Quran is important in those scenarios.