Tracking vocals, taking longer than any other instrument, seeking advice

To me they don't sound too bad especially after some processing. He could use better enunciation as other have said. Also really listen to them in the music. I bet in the music it will cover up a lot as long as he is in time which is the most important.

I think when you are too close and you want your project to be totally pro and awesome, but sometimes what you have is actually fine, your standards are just too high. From my perspective I have saved vocals waaaay worse than this.

So being your own band, try really hard not to overthink it and the let the vocalist go for it. Add distortion if you have too, focus on making it exiting and aggressive and in time, but focus less on tone.

With inexperienced vocalists, I have let them hold like an SM7 on the stand top pulled out like a stick. Angled it bent over. I also let them take an SM58 and hold it with the monitors or even PA speakers going. Or sometimes a D5 for more clarity. But with some cleaning up, gating, and have him face the speakers/pa so you have the mic null. You would be surprised how usable it sounds. And if the aggression and excitement is there, you are golden.

They have to feel comfortable so make them run around, treat it like a rehearsal or show. Some just need to hold the mic and have loud music around them. I get it.
 
these will work fine. i did the same thing as you man and my old vocalist had that same midrangey shouting thing going on. The most important thing is how he sounds in the mix with the music. At least his tone is unique and not sounding like every other randy blythe copy cat. the trick is to work with sessions back to back as soon as possible. if you keep waiting for ever in between hes going to fall out of his groove. schedule a 4 day weekend and have him track for 2-3 hours a day with nothing but rest after that. Beers come when the session is finished. thats how i went about it and these are the results i got. https://www.youtube.com/watch?v=uIXyYrzTtjw you can tell hes not the best and has that raw-mid yell thingy going on but in the end i think it turned out ok.
 
This is useable (for as far as I can judge without a context). Still for a next album I would suggest to him getting some lessons or a coach and really look at his lyrics and edit those before recording so there is space at the right time for him to breathe and stuff like that. That will also make stuff easier to record.