Thanks for your responses.
We switched to Half-Mode as suggested and I'm pleased to report that we haven't had problems all morning.
However, I'm not sure if we're seeing any benefits... (?)
On each page I see at the bottom:
"Dynamic Page Served (once) in n.nn seconds"
It seems to be generating the pages every time - it doesn't appear to be using the cache at all (?)
On the disk I can see the static html files that were created under my cache directory but these are not being updated... so maybe there is some caching going on here.
Maybe it is working and I just don't understand it...
My RewriteCond rules only refer to the supercache directory not the cache directory above... Should these rules be changed for Half-On mode?