Wow! I think I will have to respond with questions more than answers this round!
1.
I have three 6-wk-old "layer" chickens
but
They hatched within the first 4 days of September
I'm hoping that what you meant first days of August, so you really mean 6 week.
2. You haven't mentioned predator pressure - day vs night. That really impacts your options.
3.
I feel a HIGH degree of responsibility for animal care!
I agree - and one of the things I think these birds need right away is some exercise. What are the CornishCross contained in? The layers are smaller but more mobile - can they go join the meat birds for a couple hours a day at least?
Story time: My friend has some banties who due to her landlord passing, had to come and live on my farm. One was broody and wouldn't give up. We gave her regular chicken eggs and she hatched 4 on Aug. 16. They were in a tiny rabbit hutch. I have a movable crate made out of those square panels for shelving that is only one panel high, two wide, by about 6 long. It took about 4 days of training, but the group of mom + 4 will run down their ramp (or fly right off it) cross the field about 60 feet with only a little encouragement (there might be a bug or blade of grass to poke at, doncha know?) and return 6-7 hours later. It's the exercise going there and back that I consider as important as the fresh grass. They're safe from day-time predators more or less and they're locked up at night safe from night ones. It's not perfect, but it is adequate at the moment. It gives them exposure to watching for flying predators and prepares them for when they will likely have to free-range to some extent, unless I actually get multiple paddocks built which is on the list.
We also have several groups of moms with ducklings ranging from 1-3 weeks old. They get free-range time while I'm feeding/filling buckets/collecting eggs/moving portable shelters, but when I'm done and need to leave the field, they get locked back up. As they get older, they'll be allowed some free-range time when I'm not there, but we have a pair of geese which offer a bit of protection and a pair of scare crows I intentionally designed to be fairly easy to move around in an effort to keep them effective. Only the three-week-olds were incubator hatched - having a real mom does help a lot.
Hopefully this will give you some ideas of what you can look around for that could be temporary day-time housing that the birds can be trained to go with you - any sort of frame you can through a tarp over might do the job - and get them at least a little exercise so they grow up strong.