The vocals definitely don't mesh with the rest of the recording.
I had to make
an iPhone recorded vocal track work (not one of my best overall mixes, judge me lightly

), and from what I can what you have to work with is in better shape than the slightly out of sync, master track playing in the background, and pitchy take I had to use. I mention this as an example of what you can suck from a take if you break it down into smaller pieces. Mine is still not perfect or ideal, but IMO it succeeds because the vocals at least sound like they're in the same room.
Make two copies of the take.
First track - remove that out of place roomy reverb. I'll assume it's from his recording environment, so you need to use a limiter/gate to cut as much of the background echo out as you can. It sounds like a quick delay, so you'll be looking at an aggressive setting. This might result in chopping the end off some of the words or having a gated effect where things don't trail off naturally, in which case you'll need to edit the track BY HAND fading in/out before/after each word or line is spoken. Yes, it's cumbersome but that's how it's done (this is a resurrection after all, if it was easy the issue would have already been fixed/addresed). I did the by-hand method for the track I linked to. I then mixed this down so it was one continuous track again for ease of adding some compression, effects, EQ, reverb, etc. Mute this for safe keeping.
Second track (original), compress it. Add a touch of distortion or an amp sim if you want, this will be mixed conservatively to add some presence only, and because it won't be mixed in very loudly the fact you didn't correct anything won't matter since the reverb levels should be well below the level of the rest of the music. If you can hear the reverb creeping in, you're mixing this track in too much.
So now you have a cleaned up track and a compressed/gritty track for presence. EQ both tracks and do what you will to make them mesh better with the rest of the instruments. Obviously using less reverb will be key, and I would probably use some chorus on the repaired track so when you mix it with the compressed vocal track you'll have a full/rich sounding vocal.
It took me maybe an hour to get a working vocal mix. Ymmv.