With a good 'listening' knowledge of a wide variety of music, you probably already have heard all the modes. When you are experimenting with harmony and melody you have a set of rules to follow - as you're doing, but when something makes you cringe - you probably broke a rule. Although sometimes you can't quite work it out. There's also the problem of everything having multiple descriptions, so Am being used as a key, when it's really C - so one type of scale is another one anyway. In my music I seem to rather like Major7th's and minor7th's. However these also have different names too, so Dm7 becomes F6, and all the chords can be morphed into new ones. moving one note in a chord often does really nice things. Playing a melody over these chords gives you one of the Greek 'names' - but do you actually need to know this name? I'm not really sure it matters.
when you study music theory, very often it just makes the links between what you did musically and why it worked. My friend plays all the modes as practice, and very often when you hear one, you immediately think of a song that used it. I like those really bizarre complex jazz chords you often see in the books, but when you look at it, the chord is almost something much simpler, but the one extra note turns it into some really weird.