I think you're on to something. I don't think it would take much to turn this into a 70s-type song that would slide right into a yacht rock-type playlist along with songs by Christopher Cross, Ambrosia, Player, etc. That's NOT an insult! I've often said I like all kinds of musical genres, I just seek out the best in each (FWIW I saw a Christopher Cross concert and it was excellent). As to specifics:
- More consistent levels with the vocals. Check out the tips I've done about using the Gain Envelopes to create consistent vocals that amplify the human element.
- Selective use of doubling. Not at the same level as the lead vocal, but in a supporting role.
- The song is crying out for some vocal harmonies in strategic places. Your voice's timbre lends itself well to additional harmonies. If you have a hard time coming up with harmonies, copy your vocal and use Melodyne to program a harmony that sounds good. Learn it, and use your real voice to overdub it.
- Personal bias alert: I've never used saxophone in any of my music, because I don't play sax, and I just don't think it's possible to include the nuances that make for a convincing saxophone sound. That said, you got more out of that part than most people would! My "workaround" is to use a synth sound that comes close to a sax when playing sax lines. Then you still get the effect of a sax, without sounding fake. There's an example of this in my song Factory Girl (the link takes you to the solo). I use a sax sample from Presence, but modified it to sound more like a synth. It may not be your cup of tea, but you'll hear what I'm saying.
Keep at it, and be confident about your vocals. You may not realize how much potential they have.