good analysis.
yes the plugin uses the first H1 to determine the title and it uses the title to dertime if it is new or an update.
specifically changing the slug to be based on filename would not actually solve it as such, as still need a title.
what it probably needs is a fallback, as you suggest, title may be a good shout.
You have come up with some good issues, but please bear in mind, as work in this is in my spare time and ideas or changes I may choose to corporate may take some time, especially as it is holiday season.
if you are hand with php then there is a development repo you can contribute pull requests to.