I think you've got adequate answers (they address the questions you ask). I'll offer another opinion though. I hear no "grittiness." I listened to both the original mix and the dry vocals. You're coming through cleanly. I detect no artifacts of equipment or weird contributions of the room. I think Guitarman and TLW said it like I would--your own voice, recorded and played back, can be a real problem. I hate listening to myself that way. I think I sound great when I hear me through my own head...transmitted through bone and sinew with all the attendant attenuation/amplification/EQ those head structures provide. But played back to be heard as others hear me? YUK!
Some years ago, when I was still in my singing prime, I sang a duet with my brother. I kept thinking as we would practice and then as we performed before an audience, "I really don't like his voice." Mine, however, pleased me greatly. Then--horror--I heard the recording that had been done. I sounded just like my brother. Our vocal timbre is so close that our sound meshes well. Still, I just didn't like hearing it. We sound so alike. What I didn't like in his voice was strikingly in mine too. I sound like him and he like me.
You might want to record the song with another vocalist, if you can get one. Otherwise, I'd suggest leaving this song for another one or at least giving it a long rest.
Sonar Platinum, Alienware R15, i7 processor, Roland JV-1080, Yamaha KX-88, Behringer U-Phoria UMC404HD