I did a crap job of explaining the sticking points.
The problem I need to resolve: As a user, when I log back into the community after a couple of months, the Conversation feature is not usable. The counter is wrong and the dropdown shows old posts. It takes multiple clicks that aren't immediately obvious to resolve the situation. So I don't do anything and instead workaround the situation.
Mark conversations read is the best idea so far.
How else could I approach the situation? Thoughts and ideas are welcome.