My son sees Dr. Minkus. Dr. Minkus is very non-alarmist but sometimes I feel like he's too non-alarmist. His answer to everything is don't worry about it with no explanation. But he is very laid back and open to whatever you want and very non-judgmental. I know you said he doesn't accept your insurance, however, have asked to see if they will join your insurance's network? Sometimes a doctor can easily join a network and is willing to if you ask.
Where are you located? When we had our son downtown at Prentice we LOVED the pediatrician we had at the hospital -Dr. Lechmann with the Northwestern Memorial Physicians Group. We would have used him after too but he's located downtown and we live in Evanston so it wasn't convenient. He was really open and went above and beyond. He called us at 8pm one night because we had a question after he was no longer our son's doctor!
Also, when I was expecting I got a handful of recommendations in the Evanston area from friends. I still have the info so if you're interested send me a private message and I'll give you the list.
Good luck with your search!