That makes a lot of sense! Totally can do! I used to breed African Cichlids (fish) and when introducing new species, they had to have extra room, lots of hiding spots, and territories had to be disturbed. Seems very similar in method.This is where I'd change your plans. After supervised playtime I'd let them prove to me that they can get along in the run unsupervised for a couple of weeks before I tried locking them in the main coop at night with the others. Let them sleep separately for a while longer.
Your coop meets the requirements for square feet many people on this forum use for fully integrated chickens, but integration often takes more. There just isn't a lot of room in there for one to get away from another if it needs to. From your background I don't think you will have big problems being patient.
The morning after you lock them all in together at night, I'd be down there at the crack of dawn when they wake up to see how it is going, just in case. With mine that's usually just one or two mornings.
And yeah, I'm not in any rush and I'm willing to take it slow to ensure health and happiness of the chickens. I am home all day, and I usually wake up early, so this shouldn't be a problem. Mr. Tide starts crowing at 4am, so I'll know when they're up.