Hi Mark,
Not being a developer, i cannot comment on the limitations of the Joomla update system, I still do think that it isn't a wise decision to abandon it altogether as there are certain advantages that are lost (integration with backup systems, receive notifications upon logging in that an update is available,, integration with 3pd monitoring service such as watchful.li).
I do understand that this is the route that you choose, is it possible to add a module for the amin that notifies the user that there is an update (similar to the joomla update notifier)?
Thanks in advance,
Chaim