That sounds pretty good. Your playing abilities are there. Good work!
Thoughts on Singing:
This is a tough song. Lots of low/mid voicing and then it jumps up to that upper octave. You did pretty well, but I could hear the strain. I hear it in my voice too when I sing similar songs. I would do two things:
1) Select another key which will lower it by about a step or a step and a half. This will ease you voice in the upper register. However, you sacrifice your low end, so this might not work if the low just isn't there. But, listening to this, I'm betting it is.
2) Spend some time in front of the piano plunking out only the melody (no chords at all). Sing along with this and make your voice sound as much like that piano as possible. Choose syllables rather than words ("Loo Loo Loo" or "Doo Doo Doo") to sing with. If you do this and warm your voice up on the low working up to the high end, you'll get a few more semi-tones out of it and that higher register (and lower) will get easier and clearer.
Again, I think overall it is a good cut!
~DB