I really doubt it, and I am not surprised that apps didn't work. I also don't think playing a musical instrument actually gives as much insight here as you want - it's a very indirect transfer if you're learning via classical methods or if you are learning purely by reading. Jazz and contemporary methods involve a lot more "listen, then play back" rather than reading. If you want to work on ear training and theory, cross-training with some jazz or contemporary helps a lot.
The way music schools teach this is relatively brutal and annoying, with a _lot_ of repetition and testing (eg "sing a major second above this note" and "identify the interval" questions), but I am not sure any other method works. At the same time, everyone going through an ear training curriculum does pick up decent relative pitch. This can take a year or two for college music majors, so it's not exactly a casual exercise. However, I assume the major barrier to entry is not musical aptitude but willingness to put up with bullshit, because it feels like bullshit when you are doing it.
The way music schools teach this is relatively brutal and annoying, with a _lot_ of repetition and testing (eg "sing a major second above this note" and "identify the interval" questions), but I am not sure any other method works. At the same time, everyone going through an ear training curriculum does pick up decent relative pitch. This can take a year or two for college music majors, so it's not exactly a casual exercise. However, I assume the major barrier to entry is not musical aptitude but willingness to put up with bullshit, because it feels like bullshit when you are doing it.