In the end, running Apache2 with mod_python just isn't a process that is particularly kind to 256 megs of ram. I've finally moved to upgrade to a 512 virtual server instead. It gives me an odd giddy feeling to run top and see that I actually have unused ram. With this upgrade I am pretty comfortable that the recent instability of this site should be over.
I'll keep my eyes on the Apache error logs though, on the off chance that there is something more nefarious running amuch.
I also have started looking into optimizing Apache2 a bit more. As per my setup tutorial, I am running Apache2 with mod_python behind nginx. My first change has been to set "KeepAlive" to "Off". I don't serve any static files via Apache, so there seems to be many reasons to not have KeepAlive on, but no reason to have it on. So... now its off.