What I try to achieve is to house the chicks somewhere they are behind wire so they can see the others and the others can see them but they are safe from pecking. The look but don't touch. House them there long enough that they return to that place to sleep at night when you finally let them out. I let them sleep separately until they have mingled during the day for about a month. Is a full month necessary? Probably not, but it's easy with my set-up. Then after a month I'm OK with putting my chicks in the main coop at night with the adults. I'm always down there first thing to open the pop door when I do that just in case it is necessary. It never has been necessary but I have a large coop with plenty of hiding places. What I often see after they wake up is that the chicks are on the main roost when the adults are on the coop floor. My roosts are high enough that the adults can't peck them from the coop floor. Not everybody has roosts that high.
So what does this look like for my brooder-raised chicks. Two different scenarios.
My brooder is in the coop so the chicks basically grow up with the flock. When they are five weeks old and weather is appropriate I open the brooder door and walk away. After they are all out I lock the brooder. Mine also have a lot of rom outside and I have the weather where all the chickens can be outside all day every day. Even when it is really crowded I have over 60 square feet per chicken outside and sometime I have over 50 chickens. A lot of room. At night the adults put themselves to bed on the main roosts. The chicks usually don't even try to sleep on the main roosts for months. They find somewhere else to sleep but they do sleep in the main coop. As long as it is not in the nests and is somewhere safe from predators I don't care where they sleep.
Your brooder is not in the coop so you can't do this. And on size, I had a broody hen wean her chicks at three weeks. She totally left them on their own to make their way with the flock. The were not even close to the size of my five week olds and they did fine.
This is closer to your situation. When the coop is getting crowded I'll move five week olds to my grow out coop instead of just turning them loose. That grow out coop has a bit of run associated with it so the chicks and adults can see each other. After I'm sure the chicks will return to that grow out coop to sleep at night I let them roam with the rest of the flock during the day.
After they have roamed with the flock during the day without problems for a month I consider moving them back to the main coop to sleep at night. Each year is different, I go by what's actually happening instead of being married to a rigid schedule. But usually I've eaten enough older cockerels from previous hatches to make room in the main coop to move the pullets back in about when they are about 12 weeks old. I often have three or even four different aged groups of chicks in with my adults from five week olds to pullets getting ready to lay and cockerel ready to go to the freezer.
I have never lost a chick to an adult doing it this way, but some people have. I don't know what your coop looks like in size or layout. I don't know how big your area is outside or when that outside area is available to them. I don't know how any of this will work with your flock and facilities. I do understand you wanting to get them together so you have less work feeding, watering, and cleaning. My main suggestion is to have patience and go slow, but go. You don't need to wait until the pullets are laying to start integration. Let the get used to each other and give them as much room as you can.
#2 or 3 sound fine to me. Last time I integrated chicks the the coop I put them in a rat cage inside the coop at night, and by the 3rd night they followed the hens in, flew up to the roosts, so no more cage. I set the pop door to open earlier than usual (in case they had to run in the morning) and when everyone seemed fine after 5 days, pop door went back to normal opening time.