What I ended up having to do was actually:

SqlConnection.ClearAllPools();

Then assign a SqlCommand to drop the table like I was originally doing:

string sqlConn = ""; // your SQL Connection String goes here

string sqlDropTable = "If (object_id ('MyDB.dbo.MyTable') is not null) DROP MyDB.dbo.MyTable";

SqlCommand sqlDropCmd = new SqlCommand(sqlDropTable, sqlConn);

sqlDropCmd.ExecuteNonQuery();

-Tom