I don’t know how you can look at what process hung in the past, but you could install Glances and periodically monitor resources being used. The hope is that whatever caused the issue would do so gradually, for example a slow memory leak could be noticed by seeing a steady increase in memory consumption of an add-on (or whatever) before it crashes your system.
Edit: Have you thoroughly checked all logs that HA gives access to? I wonder whether there are more logs, or older logs, that aren’t exposed by HA that you might be able to look at. Also, if current logging is not good enough you can temporarily log more… this thread has some tips on that: