The following results in successful sub-second page loads.
<add name="test" connectionString="Data Source=TEST_ORACLE;User Id=user;Password=password;" />
The following subtle change to use the app pool's custom identity results in successful page loads that are 20+ times slower.
<add name="test" connectionString="Data Source=TEST_ORACLE;User Id=/;" />
It appears that I at least got the trusted connection to work. What am I missing?