First of all, I'd like to acknowledge all of the wonderful people who helped me along the way, @drumstick diva @aart and @Mrs. K . These three put up with my annoying, multiple posts. (Sorry Aart!) and tried to help as much as they could.
Now saying this I'd also like to say I'm sorry if while you read this you think, "Man, that was dumb!". I'm only on my first (now whole!) flock of 8, and I got them August 2017. Thank you once again everybody! I'd also like to mention since the pullets were not laying eggs yet, the pecking order wasn't fully established which had made it the slightest bit easier to squeeze the chicks in, since there was nothing to change.
I have 2 chicks, Terry and Chewy, that I call the 'Littles'. I rescued them and found out Chewy is a naked neck cockerel, and Terry is some type of silkie mix pullet. I have 6 pullets (my first chickens) that I call the 'Bigs'. Once the Littles were feathered enough to go outside, I grabbed my old medium sized dog cage and put it inside of the Bigs' run. Then I put the Littles in the cage with their food and water, and a couple towels to shield them from the wind. I let the Bigs into the run and they were super confused and interested, I left the chicks out there for about an hour since they weren't the warmest chicks in the world yet. I did this for the first week and later in the week started letting them stay in the cage all day.
The second week, the Littles created their own hiding space when I let them interact with the adults. It was the small opening between the look-don't-touch cage and the chicken wire run wall. It worked to let the Littles cool down after a lot of pecking, and they continuously did this for the whole week, letting the Littles out for the whole day. And then on the weekend, I put the Littles into the coop, and took out the now-filthy dog cage out, and put a simple cardboard box with holes cut out in the coop. I started by locking the door to the run and putting one or two Bigs in at a time, so the Littles wouldn't be as overwhelmed. This also made the Bigs feel less protected with less friends to back them up, and helped the chicks bond with the pullets personally. Then once every Big had their turn, I unlocked the door, allowing the Bigs to come in and out of the run as they pleased, the chicks soon learned how to get onto the roosts, and watched the adults from there. I left them like this and later that night came back to lock the run door, and saw the Littles sleeping next to the Bigs, I was so happy and woke up to find the Bigs eagerly waiting as they always do for me to open the run door.
So this was how a new chicken owner like me was able to pull off an integration with no losses. My advice? DON'T BE AFRAID TO ASK BYC MEMBERS FOR HELP!! They are the most useful tool out of everything I've ever read, plus they are super kind and understand what it's like from your point of view, especially if you ask on your state thread!
So good luck to all of you newbies out there, and don't give up!
When the chicks used their old hiding spot, above
Some of my Bigs eating mealworms, above
How I integrated my chickens in 2 weeks
The story of how I did my first integration!