Are they still using a heat source when they are in the house? If so, you need to get them off that first. I wouldn't just evict them at this point. They are too dependent on the heat (if they are still using it) to just put them out, although I did just that with my first set of chicks when they were 5.5 weeks old and they suffered no ill effects. Hey, it was them or me!

Integrating when they are so big will be your main problem, I think. Feathered, they can warm themselves and each other pretty well. But integration when they are close to adult size comes with it's own set of issues. But until you start letting them outside regularly and for extended periods, they will never get used to it out there, so I guess I'd just take a deep breath and dive in. Not the advice most folks would give, but that's mine. You can put a "huddle box" out there....it's just a cardboard box placed open side down, with fresh bedding in it and a chick sized hole cut into the side. You may have to encourage them to use it by kinda stuffing them under it a few times, but they can escape adults and huddle to keep warm in it if you opt to just put them out now.
I am the last person to be able to help with integrating older chicks with adults.

Frankly, I've never done it. I've read about how to do it...but I've never done it. I brood outdoors in a pen around the adults from the start, and use @azygous
portal system to let them mingle, so I've never had an issue. Adults don't seem to see little chicks as a threat to the flock dynamic so they accept them pretty quickly, especially if they see them and are around them constantly. Having places to escape any unwanted attention is crucial. I use the portal door system that @azygous
introduced - small doors in the brooder pen that can be opened and closed. I also have a huge hollow log on the opposite side of the run. It's cut in half with the hollow side down and they duck under there if they think they are too far from the brooder to get back in. Like the doors, the adults don't fit to "get 'em" so chicks feel totally safe. Multiple feed and water stations help tremendously.
I hope someone with more experience integrating older chicks will chime in here because I'm wingin' it! Good luck!