Cheeriosok, some years ago I realized that there were approaches and ways, both for learning to play an instrument, and approaching music itself. My background is this. I played instruments self-taught most of my life. I finally took lessons on another instrument as an adult and when things went awry over time, that is when I realized this thing about approaches and ways. I went back to piano, (originally self-taught in childhood, abandoned for years), and came upon a teacher who gave me these missing things.
Here are some of the principles I learned. I agree with them, because they have worked for me, and when I first learned of them, they went in the direction that I had started to sense.
First, the way you are practising: starting at the beginning, going on until it gets dicey and then going back - is not a good way to practice. I used to do that myself, and it's amateurish and ineffective. Your playing probably sounds progressively weaker as you go on, since you are practising the new parts the least that way.
1. Subdivide your piece into sections, and those sections into smaller chunks. It is a good idea to work on difficult sections first, and/or start at the end of your section, so that you are moving forward into the last thing mastered, so that as you play, it becomes progressively stronger instead of weaker.
2. Within your sections and chunks, you may want to work on a few elements, and add elements. Playing the correct notes with good fingering and ease of motion contains several elements. The principle is "You can only concentrate on one new thing at a time." This way your focus is not scattered. When this first element-set is solid, so that you can rely on it, add another element like dynamics or whatever. With advanced music you need to do some planning ahead.
Playing music is also an oxymoron. If you work mainly based on "feeling" or "sensing", "intuitively", it may come across as sloppy and uncontrolled - or running away on you time-wise. Otoh, there are students who sound like mechanical wind-up dolls. However, if you work deliberately, and in a sense mechanically to get the foundations into the sections of your pieces, letting go of "feeling", and then allow feeling to come in again - but intelligently and measured - your playing will gain new dimensions and an added quality.
These are the things I learned, which have helped me immeasurably.