I think you've received much better recording advice for this music from the others (who are experienced in such things... everything I said was purely theoretical guesswork) but they may have indeed glossed over the need for 4 vocalists to cover material written for much more vocalists (like harmonies, group vocals, etc).
Not entirely though. They allude to ways to get those extra harmonies and doubles in there.
It's a shame to waste a good natural cathedral recording environment but since you are going to be layering performances a dry/small room/close mic recordings of each vocalist performing differnt parts and/or using pitch shifting to create the harmonies, to me, would be a more flexible and manageable approach. Note: If the vocalists can record the extra parts properly it would be way better than pitch shifting.
Harmonies are recorded like this all the time for commercial stuff using a single vocalist (I've done it myself back when I actually recorded my own vocals). With close micing in a dry(er) room, layering the parts/harmonies with multiple passes (and making sure to get multiple takes) you can do a ton of stuff in post production.
With just that you can correct the individual close mic'd takes as needed and then add virtual room reverb to mimic the cathedral.
Then maybe do some takes of the whole choir IN the Cathedral to blend in... or maybe even start with those as bed tracks for the dry close mic recordings for your singers to track to. So record the whole group in the cathedral together, maybe with more of a room mic set up for a couple takes/harmony variations. Then record each singer close mic's in a dryer environment (like a smaller room or in isolation one at a time).
Use the cathedral recording as a reference to the room sound and go through the mountains of convolution reverbs (or just tweak non convo reverbs/delays to match it as best as possible) then blend it all to taste.
If you get all the parts, in time, in all these various configurations you can do pretty much anything you want in post production.
Another thing to consider is maybe if your mics aren't all the same then try switching around the mics between the vocalists to get a take of each singer on each mic which might provide some nice variation for group vocal dynamics (like the same part sung multiple times through different mics mic give the illusion of more/different singers instead of the same singer through the same mic every time).
Panning/EQ/chorus and stereo effects can help fill out the "full" choir sound as well (again something that can be played with in post prod if you have enough takes from everyone).
Using pitch correction/humanization on the same tracks to acheive the choir effect really isn't going to be as good as actually getting the singers to perform the doubles/harmonies so get as many as you can.
Sounds like you may only have access to them for brief time (which is usually the case with live tracking) so do what you can with the artists while you have them. If some have to leave but others can stick around (or maybe you can get extra sessions with anyone later) just keep going until throats are raw or it's time for nature to take over (food/sleep/etc).
Again... just some THEORETICAL thoughts from a non pro.
The other fellows who have commenting have actually recorded this type of stuff so pay close attention to the techniques they described to actually capture the sound.
Cheers and have fun.
Edit: and yes... tlw was totally rocking the concept. He's a smart dude.