Well, there aren't any DIII's that have a lot of players drafted.
With that said, schools having probably the most success over the last several years include Trinity College, JHU, Emory, Marietta, Chapman, Pomona-Pitzer, Cortland St., Montclair St., TCNJ,players from the Wisconsin and Minnesota schools, UT-Tyler and Trinity U(Tx.).
You are absolutely correct about most DIII draftees being pitchers.
Our son was a position player in college..shortstop.
He ended up playing 2b, short and 3b and his versatility was a major factor in his getting playing time and earning his spot and innings.
What I remember about his scouting report included a plus arm, soft hands,good speed, contact hitter and the MLB report made a point of including comments on him being a player who loves the game, loves to play, plays hard and loves to compete.
From what we learned, the scouts who didn't think our son projected did so on the hitting part.
In the end, he proved them wrong. In his 1st full Milb season, he had the 2nd most hits in his entire organization. However, when you recognize what I posted earlier about DIII stats, I fully understand how tough a projection it could be for scouts to look at AB's at DIII and project those into what they mean in Milb.