pianoplayer,
I still don't know the specific parts you are rushing or slowing down.
60 bpm is actually a good tempo for this piece though.
It is an easy piece to lose the proper tempo though because there are times where you are playing a straight forward melody with left hand accompaniment, and then it switches to right hand alone, or left hand doubling the melody of the right hand.
As you listen to your recordings of this piece is it the same sections that rush or slow down? If it is the same sections, concentrate on them. Practice the preceding section through the sections where the tempo problem occurs, and try to maintain a steady tempo. Keep that tempo in your head as you are doing this.
Another thing you could try is subdivide the beat. Instead of 60 beats per measure with the beat as a quarter note, try thinking 120 beats per measure with the eight note as the beat. I don't like to recommend that too much because it is not a very musical solution, and goes contrary to the actual rhythmic pulse of the piece, but if it gets you "over the hump," it might be worth a try.