Is it possible to set a default page size on the System Logging window and have that setting retained across invocations and restarts?
If so, how?

the page size on the logging view isn't persisted at all. The logging view is stateless and the record offset and page size is passed back to the client for update/re-submission. So the setting will be persisted across restarts if you keep the view open in your browser.

However if you wish to change the default page size when for when ever you go to that view you can edit the file

<install>/modules/ext-introspect-1.2.2.jar!/org/ten60/netkernel/introspect/reports/log.bsh

this contains the line:

records = 20;

which you can change to any value.

Cheers,
Tony