Okay, I know this is a long post, but I've had probably half a dozen cats in my life and I've done the same with each of them with good success.
Every time I've brought a new cat home, whether it was completely tame from someone else's home, or if it showed up wild on my doorstep.... whether it was the only cat coming into a clean area, or my second or third cat joining the gang... they have all done what yours are doing. (maybe not as long, but certainly for a few days at least). And a cat who is scared can go a long time without eating, drinking, or using a litter box. My experience has also taught me that the one you had to catch will likely be the hardest one to win back over to you. I happened to be holding a new kitten when another cat walked out in front of me and the kitten freaked. Instinctively I tried to hold it close and assure it with my presence. Wrong. This cat that never before had a problem letting me pick it up and hold it, took a year before it would let me pick it up at all, and now years later, I still have to be careful that no other cats are around when I pick her up or she freaks and I end up having to win back her trust all over again.
What I do is just sit in the middle of the room (or leaning against the wall on the edge of the room) and let them come to you. If you have to sit on a pillow and quietly read a book all day, fine. Do it. If you don't have whole days to give, then do at least some time every day. As much time as you can give. Put their food, water, and litter box in the same room but as far away from yourself and as close to them as possible. They probably won't use them in front of you but that's okay. If they come out or move at all, you do nothing. And when they eventually come out and investigate you, which they will eventually do (even if it takes a week or two) you still do NOTHING. You let them walk all around you, sniff you, rub on you, sit a foot away from you and stare for an hour. Whatever they want to do, you have to be patient enough to let them. It's the only way I know of to overcome their fear. They have got to get it through their heads that you are just "there" and it's okay. And any reaching out or initiating you do will often just deepen their fear, not relieve it.
Once they come out a couple of times with you sitting in the same room, you can stop doing that and just go about your business but try to be mindful when you are near them and be extra calm and quiet. They will eventually come out more and more. And at some point they will slowly, thoroughly explore every inch of their new home. Cats rely on a knowledge of their territory for safety, even housecats.
When they do start approaching you, slowly hold out your hand flat, palm up, and let them sniff, rub against you, etc. without really trying to reach out and pet them in return. Just curl your fingers a bit and they should naturally try to scratch their jawline against your fingers and rub their forheads against you (marking you with the scent glands in front of their ears, so you belong to them now). Once they aren't afraid to come close to you and let you touch them, a sure way to win over most cats is to scratch them on the back of the neck and between the shoulder blades. And when they are really trusting of you, stroke their ears between your thumb and finger. You wouldn't think they would like that but mine all squint their eyes shut, jut their chin out, and purr their loudest when they are getting their ears stroked. (reminds me of the Ferengi on Deep Space Nine, lol)
Oh, and I do know someone who had good success with her cat by putting a small pompom of yarn on the end of a string on the end of a stick, and dragging it on the ground in front of the cat. The whole contraption was long enough that she wasn't really "close" to where the cat was and it got so excited by the chase-toy that it forgot about her in very little time. I don't know if this will work with your kitties since they've already been a little stressed. Every cat is a different personality!!
Good luck!