The dust is FINALLY settling regarding the storage cleaning API and extension developers incorporating the latest updates.
The developers of Cookie AutoDelete (CAD) have just released version 3.5.0 of the extension for Firefox and among the list of changes is the ability to automatically clear a great deal of stored data on a per-domain/tab basis, including indexedDB data. If the 'Enable Automatic Cleaning' option is enabled, then all selected site data will be cleared upon leaving the domain (closing all its open tabs) after a configured delay.
You can read more about this release on the 'arkenfox' site in Martin's article, Cookie AutoDelete 3.5.0 extension gets massive cleanup improvements and you can install CAD from its AMO page.
I'm testing CAD now and will add it to one or both of my Firefox configuration guides if all seems OK, as well as my recommended extensions page.