I've switched the server to nginx. I don't have too many htaccess-based rules, and overall the Apache2 configuration was very simple to begin with. I installed php5-fpm, followed tutorials on configuring nginx (moving what'll be common among 15ish virtual hosts into a separate file), configured proxying for XMPP BOSH and finally improving SSL security.
Apache2 now sleeps quietly and the RAM usage is down a bit. Hopefully the server won't suffer any more hard crashes due to lack of RAM like it did immediately after I moved to the new host.
Overall, nginx seems like a much lighter and easier to understand solution for my very simple needs; if you're running a simple server, I recommend it (as long as you read a bit about its security, if you intend to use it for serving PHP!).