Well, I wasn't trying to get an OLE DB connection working so much as trying to get anything to work.
As it turned out (thanks to Nick Olivo of SmartBear support), the easy way to generate a connection string is to use the wizard in the database table checker keyword checkpoint. With that, I was able to generate two strings that worked. The first uses the SQL 10 native client; the second uses an ODBC connection.
"Provider=SQLNCLI10.1;Integrated Security=SSPI;Persist Security Info=False;User ID=\"\";Initial Catalog=MyDb;Data Source=(local)\\SQLEXPRESS;Initial File Name=\"\";Server SPN=\"\""
"Provider=MSDASQL.1;Persist Security Info=False;Data Source=MyOdbcConnection"
There really ought to be an article on connection strings that points out this technique. I spent a lot of time trying to get this to work.