Although the "music as a language" metaphor is overdone and often inaccurately used, I think it applies here. Basically, it seems that you have the information and understanding, it's now just a question of fluency and getting quicker at identifying the information.
As such---just like learning a foreign language---you want to reach the point where you don't have to think about every little detail, but instead you just instantly recognize materials.
At your stage, you might stop and think "well, I know that chord is some type of predominant, it sounded like there was chromaticism, scale-degree 4 was in the bass, and oh, that was the lowered second scale degree, so that was a Neapolitan chord!" By the time you've gone through the thought process, the music is already in the next phrase.
You understandably want that process to go more quickly. For me, this instant recognition came with score study. By looking at pieces and recognizing where the Neapolitans were, where the applied chords were, where the mode mixture was, what various large melodic leaps were, etc., I was able to build an inventory in my mind of what these concepts sounded like. Now when I hear them, I can recognize them in real time.
