Yeah, don't stop singing. If you can address the pitch, I think you could be quite good. The sound of your voice itself is great for this kind of tune. I like it. Kind of reminds me of the guy from Built to Spill a little. Cool tune too. Personally, I really liked the melodies.
I heard the first few notes and thought, "wait, he doesn't sound flat?" but shortly after, it became apparent what the issue was, and you already noted you're aware, so that helps at least.
One thing that has helped me to some extent is tracking the vocals with the backing music lower than I'd normally like so I can hear my voice really clearly above all else. I also mute a lot of instruments that might get in the way of me hearing my own pitch...like the bass. Obviously you need at least something in there as guide, but try to keep in minimal while you monitor during vocal tracking. Sometimes I think one hears the bass or a guitar filling in the correct pitch and it fools you into thinking you're hitting it as well. Just some thoughts...