For all of its strengths as an instrument, piano has some drawbacks for learning to read traditional staff, as there isn't an (obvious-to-the-uninitiated) differentiation between notes or across octaves (you just sit in front of a wide line of keys). I think I learned to read first on a recorder, where you can develop a more intuitive link between fingerings and notes (especially as the first note you learn is the B dead in the center of the treble staff).

I'd suggest a few paths to learning the note positioning:

- If you're already comfortable with note locations on the keyboard, don't be afraid of the line/space mnemonics. If they get you to where you're making ID's faster in the parts of the staff where your hands normally live, it can make life much easier, and you can easily extend from there. There are really only ~26 note/staff associations to learn that will cover the majority of the music you'll see day to day (with octave shifts) and knowing a few will make the rest come more easily.

- Similarly (and I think this is the way piano is taught to beginners, but it's been a long time) you can make a lot of progress by starting your thumbs on middle C, which is dead between the staves and operating from there to play simple music. As you play and read more music, you'll find yourself starting to recognize the locations of more notes across the staff, until they all come to you intuitively.