So you have six 8-week-old chicks and twenty 4-week-olds. I assume the "hens" you mentioned are the 8-week-olds.
I looked at your ten-day forecast (thanks for including your location). The lowest temperature I saw was 37* F, not too bad. I've had 5-1/2-week-olds go through nights in the mid 20's F with no supplemental heat. Others say they've done that a week earlier. I would plan on getting them out of your house earlier than 3 weeks from now even if you cannot provide supplemental heat out there. I know how uncertain ten day forecasts are but they should e able to go outside without any heat in another week.
If you can safely provide heat in the coop, you can move them out now. My brooder is in the coop, I put them there straight out of the incubator, even when the outside temperature is below freezing. I keep one end of the brooder toasty warm but let the far end cool off as it will. Sometimes there is ice on that end. To me the biggest challenge of brooding outside is the temperature swings. You want one area warm enough in the coldest conditions and an area cool enough in the warmest conditions, the chicks are really good at selecting where they want to be if they have a choice. I've gone between below freezing to over 70* F in 36 hours, quite a swing. If you are brooding in your house you don't have to deal with that. But I understand wanting them out NOW!
20 chicks is a lot of chicks but that's the typical size of my broods. I use a heat lamp securely wired into place so it can't fall to provide heat. Wire is important. Do not depend on a clamp and do nut use string or plastic that can burn or melt. There are other ways to provide heat, heating pads or heat plates work great. But twenty 4-week-old chicks need a fairly large warm area, especially to sleep. If you don't like a heat lamp you might look at a hover. That's basically a shallow box open at the bottom that traps heat. Warm air rises and gets trapped underneath. You can handle a lot of chicks with one of those but by the time you get one built and working you probably won't need it unless the material is there and you give it a high priority. A heat pad or heat plate could provide that heat in a hover.
It's been a while since I read Aart's article. She tends to overcomplicate things and micromanage more than I do but her methods also tend to work. Think on her methods and how you can adjust those to your situation. They are good methods.
Your coop is a good size but the run may prove small. You can improve the quality of your run by adding clutter. That's Aart's "places to hide". It can help in the coop too. I have a lot more room outside than you do, my adults tend to go outside in the morning and not go back to the coop all day except to lay as long as a cold wind is not blowing.
My definition of a successful integration is that no one gets hurt. That is it. Mine tend to stay apart by age until they all mature, which is fine. When a less mature chicken invades the personal space of a more mature chicken they just might get pecked. It usually doesn't take that long for the younger ones to learn to avoid the older, day and night. It doesn't always work that way, sometimes they merge quite well. Yours may be close enough in age that they do not stay apart. I'd think the sooner you try that the more likely it is to work.
Sometimes it works to just put them together and let them go. It can be that easy. I have more than 50 square feet per chicken outside even when I'm crowded, I think that helps a lot. You can try that but I'm not sure you have the room. I'd definitely want a day I could spend a lot of time observing and be ready to intervene.
I would have a place prepared I could instantly isolate them if necessary, you may need it. My basic steps mirror Aart's if that doesn't work. House them across wire for a while, provide separate eating and feeding stations far apart, provide as much room as you can, and provide clutter. As much as I can I let mine manage merging by themselves. If they want to stay apart, let them, day and night. Try not to force them into small areas together.
Sometimes this does go really easily even if you don't follow all these suggestions. But sometimes it doesn't and you need to work harder. But it can be done.
Good luck!
