Upon further testing, I discovered that changing $session_management_via = "session_cookie"; to $session_management_via = "key"; fixes the problem with Safari.
The defaults.config file in 2.16 says "session management using cookies is more appropriate when external authentication systems are used, e.g., LDAP, LTIBasic, etc.", and session cookie now seems to be the default in 2.16, but this is what may be causing the issue with Safari. I don't know all of the ramifications, however, of using "key" rather than "session_cookie" for the session management.
The defaults.config file in 2.16 says "session management using cookies is more appropriate when external authentication systems are used, e.g., LDAP, LTIBasic, etc.", and session cookie now seems to be the default in 2.16, but this is what may be causing the issue with Safari. I don't know all of the ramifications, however, of using "key" rather than "session_cookie" for the session management.