While not directly related to your answer our HS installed turf on our football field about 5 years. The total cost for project was right about $1M. I did a quick google and it appears that the cost to turn an infield is somewhere around $300,000+. With estimates of about $750,000+ for an entire field. Based on what we payed for the football field these estimates seem about right.
I would expect that a baseball field would typically be MORE expensive than a football field. Unless that $1M turned into paying for other things within the complex such as the track. A baseball field is often bigger than a baseball, and not just a little bit either.
Coach_Sampson has shown a couple pics of some in the St. Louis area. Coach, you may actually call Edwardsville High School and see what they can tell you. Their JV field is turfed on the infield. Also, SIU-Edwardsville has a turf infield and GCS Ballpark is all turf. I think that TR Hughes Ballpark in O'Fallon, MO will be turf in the next couple of years. O'Fallon, IL also has turf for their baseball field, but I can't remember if it's the whole field or just the infield.
My school is currently putting together estimates to turf our baseball field. Our football field already has it, but our baseball field holds water big-time so they are looking at that investment. Last I was told, they were looking around $1.1-1.2M but I don't know if they were adding any other projects to it or not. This is down in Dallas, TX. Quite a few private high schools apparently have turf baseball fields already...
I was trying to stay with the high school leve but I know that GCS and Lindenwood University have full turf. I didn't know about the Illinois area schools as we don't really get over there to play a lot. The first field that I had posted is actually a team in our conference.
To get this done will be a long shot to say the least. The athletic facilities are the last thing the school worries about. Heck I can't even get the maintance guy to cut my grass the way I want it done and they will only cut the grass 1 time a week. I am not allowed to use any of the equipment to cut the grass on my own.