Couple of things. First, you're pretty good. Really quite good. For me the sound quality (maybe my speakers) made it a bit hard to hear clearly some of your words but I think for example, 'they all went away' for the 'th' I could hear a hint of a 'd' instead of a pure 'th'. This always causes a problem with non native speakers. Has to do with placement of the tongue behind the front teeth which causes the hint of a 'd'. think about where your tongue is placed when you pronounce the 'th'.
If you spent a few months immersed in an American setting you would have no trouble 'tweaking' your accent.
Having said this, I know you must realize there are regional accents in America, deep South, Midwest, New England, New York, Bronx, Brooklyn and more. So a simple word like 'water' can have a slightly different sound or not so slight, depending on where you were raised. Which I can't explain in writing! To me your accent has more of an eastern seaboard flavor. Often recommendations are to try and listen to American language radio which is excellent but one must realize that broadcasters generally do not have regional accents or really any accent and all sound pretty much alike...bland. This is so everyone can understand them. LOL!
I think your accent improved when you started reading faster and at a more normal speaking pace. And when you were not reading but just speaking about what you were going to do. That sounded more real.
Were your English teachers native speakers?