Outside of having the DBA alter the DAUDITNEW table with additional indexes, I use the EVENTID. I have a query that I run once a month that returns the 1st and last EVENTID for each Month. The previous months don't change. I use this table to execute some with ranges that I would normally(previously) use the AUDITDATE field. Using that with a TO_CHAR function adds enormous time and requires searching through all too many rows unnecessarily. I can specify a range or a starting EVENTID since that field is indexed and has no need of using a Function on it to parce any part of it.
I've only started using this approach, but it works well. Perhaps there's a better way or even a way to dynamically retrieve these values within a given query (perhaps through a user-created Oracle Function). I'm not an Oracle expert, so I bow out after that.