I agree you've got something going on. Here are my ideas:
If my math is right, you've got close to 60 birds now in a 600 foot enclosure which will be approaching the limit for that enclosure (10 square feet per bird for ranging when mature). Be aware you will deal with more issues of health management the more numbers you try to maintain especially in a closed, limited environment. You may have to accept some loss.
You began with 14 RSL who were laying in August, and you've had them for 5 months, so these were mature birds (now at least 1 year old?). You loss 7 over that time. That means you introduced mature birds to a new environment. Birds often have latent illness which can be triggered with stress caused by a move, and possibly you had a viral or bacterial outbreak, or more likely coccidiosis lurking in the RSL's (slowing working through) as they became infected by your soil (coccidia live in all soil, and there are different strains, each farm is unique even across town or neighborhood).
The other thought, if they were completely healthy looking and then dead the next morning, is there is something in your free range that is toxic to them. Do a plant check in your environment, or toxic pesticides as the other poster mentioned.
If no toxins, then I am back to Coccidiosis as a real potential since being a new owner you might not be picking up on subtle signs of infection before it reaches crisis. Birds can go down very quickly with Coccidiosis. Coccdiosis does not always produce bloody poo but can first present as fluffed, rumpled, a bit lethargic, but still foraging, then suddenly dead in 2 days. I always put newly transitioned birds onto medicated feed for at least 2 weeks, better a month to help them transition and prevent coccidiosis. (Amprolium medicated feed is fine for eggs....there is no withdrawal) .
Next you added smaller, younger chicks, so you've got mixed ages of very young (month old) with older, possibly sick. Not a good idea even with totally healthy birds. Those ages are too mixed. Your babies haven't built up strong immune systems yet, and they are likely being hazed and even more stressed by the older birds. Industry standard is to not introduce pullets to an established flock until 12 weeks of age up to 24 (to help prevent Marek's and other disease outbreaks, which is sadly, another thought). Your chicks could also have brought in something anew to the flock, viral or bacterial, or new strain of coccidia. As your instincts told you, one week of isolation was not enough!
Further, feeding layer feed to baby chicks is way too much calcium for babies! You will shut their kidneys down with that! The babies would be best on medicated chick start, and separate, or a mixed age flock needs to be on a flock raiser with calcite grit or oyster shell free feed for the older, laying hens.
At this point, I would consider putting some Sulmet in the water for a few days (full dose 2 days, half dose 4 days, according to bottle). That would clear up both coccidiosis and the common gram negative bacteria that grows quickly in heavily populated pens. If not that, then at least put Apple Cider Vinegar (raw, with the mother, no metal containers) in the water, a blop in the bucket. That will help acidify their guts to help their immune systems. Probiotics in yogurt is also helpful.
I would also expect losses in the young ones as I agree they are likely still too young for ambient outdoor cold temperatures and definitely any wet environment. Many would still be under a heat lamp until 4 weeks, then slowly transitioned until fully feathered at about 6 weeks.
Your birds may be dying from ammonia build up if that carpet is preventing air flow. While you do not want cold wind/draft, especially with wet, you must have good air flow as birds produce an alarming amount of ammonia and moisture. With that number of birds now, poo will build up very quickly. Once a week clean out may not be often enough. You may need to rake daily, clean weekly. Mold might be creeping in. Straw here, in Oregon, molds very quickly. It is my least favorite bedding due to that problem. I prefer pine shavings (which some think is harmful due to the oils, but I have used it a lot and never had an issue and it keeps down mold and other yuckies).
With those kinds of losses, you've got too many birds in the wrong environment. I think some investigation and deep thinking should set your situation right.
Keeping chickens is definitely a learning curve, and you jumped in the pool at the deep end with large numbers. That always multiplies the problems.
Keep us posted and good luck.
LofMc