After you are able to narrow down the 10 a bit based on what others have suggested, I might also just call them to see if they would be open to a quick chat. I would ask what they thought of certain medications and their willingness to try them with your DD. I'm sure you have done research already and know what you think might work best.
I have not worked with a child psychiatrist before but I did this with my neurologist. I went in with a spreadsheet of several medications, and had columns for side effects, pregnancy rating, etc. and I told her which one I thought was the best to try for me. My old neurologist would not have responded to that well. But I have always felt completely respected by my new (7 or so years with her) neurologist and she has been willing to work with me on dosage and different medications based on my own research. It has also allowed me to trust her more when she suggests something different because I know she is willing to try things too.
I imagine that child psychiatrists may be more used to this kind of patient involvement by way of the parents, but I would want to make sure the new doctor was VERY open to suggestions about medications, as it sounds like that is exactly what you are looking for.