My first ideas was if dnsmasq was writting logs to /tmp (tempfs in memory) and you tail the log and place into SQLite (which can be on USB, as it should collaspe smaller), then if you flush the logs hourly it will really reduce disk wear.
That being said, as a user you would need to turn off diversion's weekly stats email, since the dnsmasq logs would not survive long enough for that feature, but your sqlite would be able to reproduce all you need for stats.
You need the date perhaps, but not the full timestamp (minute/hour/seconds), so perhaps collapse this down to:
<day><requesting IP><requested site><response><count>
The DB will greatly slow down in growth, and your stats are still useful.
Either way, even if you don't think this make sense, thank you. Would you perhaps have add a feature to flush the logs regularly? If diversion has that feature I haven't found it. Once this is in SQLite it is much better than the raw logs