One thing jumped out at me -- you have a date on the calendar for when you will talk to your daughter, but no date on the calendar for when your soon-to-be-ex will move out. He's making progress, yes, by even looking at other places, but he could stretch that process out forever, and his strong tendency toward denial means he probably will. While it's good that you finally had a talk with him as you did, and that he's working on one specific place, if there is no agreement between you on an actual move-out date, he sounds like he's likely to linger and make excuses: "The place I liked fell through so I have to start looking again." "I can't find a place in the right location so I can see Daughter and take her to school." "I found a possible place but they want X, Y and Z." And so on for ages.
Set. A. Date. It needs to hold even if he doesn't have a place to be and you need to be clear that if he stays and stays it is only hurting your child.
You were very wise to tell him that though things are friendly right now, you and he both need to consider that times may come when things are not friendly. You are being realistic and he is, as you note, still in denial even after your talk. He needs the reality of a move-out date, followed by the reality of your presenting him with empty boxes to pack one week before that date. If you worry that he is going to pull a "We need to get back together, you know it's best for Daughter" routine as the day approaches -- stick to your guns and stick to the idea that what daughter needs is firm certainty even if that means the certainty that dad doesn't live there any more.
I can't remember from your other post, are you getting any counseling or therapy through all this? Please don't hesitate -- a counselor could help you have the strength to ensure your ex sticks to a departure date. And please line up a counselor for your daughter! There are ones out there who specialize in working with young children during divorces. Good play therapy could help her through what will be a long and difficult time.