OK! I just listened to the first two bars and stopped: Sarah McGlaughlin's piano comping style...relaxed and gospelly...with a much more robust piano sound...the tack hammers are gone. Going back in great anticipation....
Well, the vocals sound a lot better, too. And the longer part of solo vocal w/o harmony is about 90% spot-on. But there are times when you're not nailing the pitches...sliding up and down...OK if you can do it quickly enough...
Your melody consists of step-wise scalar lines, mostly. What it need is more intervallic leapishness to make it less flaccid...more interesting. Sarah McGlaughlin is a good study in interesting melody. Singing a lot more chord-tones in leaps of thirds, fourths and fifths....translates to strength and memorability. It's not something you can so much 'craft', but something you have to be inspired to 'hear', and transcribe from your imagination. Listening to good vocal melody, and playing it on your instrument to give you a 'picture'...visual, on the keys, and auditory, might help get some juices flowing in your brain's 'melody lobe'...so to speak.....without having to delve into the theory and such. I'd also suggest listening to, and learning to sing, classical melodies..Bach and Mozart, etc. Melodies never were made stronger or more beautiful. It's brain-train!
Now the intonation thing.
A singing coach might be a worthwhile investment...focusing on ear/voice pitch acuity. There are exercises. It's all training. Your so close. You need some professional guidance to make the most of what you've got. And you do have a lot......but inconsistantly. A lot of the skill of maintaing pitch, breathing, enunciating......all a mind-game. A good coach can cue you in to a lot of what should be going on in your head and body. After the exercises and learning, you go on auto-pilot and let emotion drive the hotrod with fine-tuned suspension and motor: you watch the track, and let the car do its thing, y'know?
Now the harmony thing. The harmonies are awkward. A lot more parellellism is needed...so you don't end up singing montarily in octaves...which makes the intonation problem really obvious. Practice parts over the melody.....work the harmony very close to the contours of the melody...maintaining a very similar shape and intervallic range.
Try different notes....record and listen. Or have a friend who is a gifted harmonizer derive some parts for you beyond what you can conjure.....surely there are a couple friends in the church choir?? Learn those parts, and you'll develop an organic feel for what works, I think. I got my best training working out doo-whoppers in an acappella quartet a long time ago. Form a group like that to have some fun and learning with. Great schoolin'. Gospel tunes like Amazing Grace...whatever. You work them out. And someone of the group with some technical training will get you all communicating such that you'll learn what thirds, fourths and fifths...suspensions, etc....sound like. It's the voice/brain thing that develops.
Anyway...huge improvements!! Keep going! I love the piano, and those stretches where you sing like an angel.
If you're serious about developing this craft...and you should be...it's time to get to serious work. Your raw gifts and drive to create ...and exponentially-improving recording ears...are worth the investment. MHO