It should be possible to obtain the set of property values shown on any of the Configuration > Servers and Sites > Default Server Settings > <tab> pages by sending a GET request to:
/json/global-config/servers/server-default/properties/<tab>
(where <tab> can be any of the following: general, security, cts, advanced, session, uma, sdk, directoryconfiguration).
Unfortunately, attempts to do so fail for all cases except the 'advanced' tab.
For general, security, cts, session, uma, and sdk tabs, a response is generated but it doesn't include any values.
For the directoryconfiguration tab, an Internal Server Error occurs.