fw log does sound like it's potentially what you're looking for.
But as Tomer suggested, I'd still keep the Log Exporter in mind as a viable option.
You can set it up to export only audit logs, and limit it to export to 30 days back.
Once per month turn it on to have it export the past 30 days, or leave it running ( and use the reexport flag when needed).
Both the log exporter and 'fw log' can be made to work for this use case.
The log exporter will need a receiving server, which is either a plus or minus depending on your environment, and the fw log will probably need a bit more tinkering with the output (but you'll probably have to do this in any case to parse the information).
Neither option is ideal for this use case, but both can be made to work. Off the top of my head, I don't see a clear advantage to either one.
I'd start tinkering with both of them and see if one of them comes out the clear winner.
Good luck, and post back here if you need help with implementing this.