It took mine time to transition as well. If I was out there with them they would be a little braver and come out. Mine were a little older though because I have bigger chicks that weren't so friendly with them. I built a mini coop for the look but don't touch approach because regular attempts at integrating didn't work (kept them in the mini coop for almost a month). Once I let them out of the mini coop and put them in the coop they hovered in there unless I was out. Then they would step just outside the door into the run part. It went like that for abut 2wks before they finally got brave enough to venture out all the way. Now they're finally out for periods of time with the bigs, and MOST of the time the bigs leave them be. I still have to stay out there and monitor during treat time though because I have 2 cochins that are little buggers lol. With food and water though, I put out an extra food and water container in the run which seems to have helped with the food/water issues.
I go out multiple times during the day, so during the time where they were staying in the coop a lot, they would come out for little bits of time throughout the day while I was out there.
Oh, also, do you have a "safe place" in the run where they can go if they need to to get away and feel less threatened/overwhelmed? I put something out for mine (it's just 2 chairs, but it works) and they have gone under them at times instead of running back to the coop.