Hi Emma - archiving sweeps out the session and log tables, and I don't think there is a way to change that. The only workaround I can think of is to report before the archiving takes place, but I suspect you've already considered that one. You can reinstate archived log files back into the DB, but that's a more cumbersome option.
There's a feature called Data Gateways you may want to take a look at. It's a means of pushing logs (and other stuff) to an external data store like Splunk, Elastic or a 3rd party DB. It runs on the app server and would push logs in real time, so before archiving was able to delete them.