Thanks for confirmation. 64GB -- that ought to do it, though I'd worry about endurance of the card and failure there taking down DNS.
Edit: From this post it seems that moving the location of those files is not possible, nor would you want to, for performance reasons in addition to endurance reasons in the case of a card.
Also from the post linked above, suggestions given were to shorten the period for the stats to <24h or increase the size of shm. In my case roughly speaking it looks like if I adjust either by a factor of 3 then I'd make it through an outage without DNS going into a crash loop. That's very doable -- increasing container shm to 256m or 512m is no problem, and is what I'll try. Though for a critical use case (not a homelab) it seems like there ought to be some proactive management around it -- DNS getting borked due to external factors is no bueno.