I manually moderate the voicemails and run a script locally to build out a static site and upload it to Neocities. The site is relatively fresh (created within the past year); it just hasn't seen much traffic yet.
I'm not really sure to be honest. The traffic today has me stepping away from work occasionally to process calls in little batches :) I would probably just streamline the moderation process to make it a bit easier. For various reasons I wouldn't want it to be completely automatic (for one I just like to listen to the messages).