When you say "final inventory" I assume you mean the "final account." If the court needs to approve the account, then the executor would need to wait until that approval has been obtained. If the interested parties waive the hearing, then the distribution can be made, pretty much at any time.
You are in the ballpark at this point, of when an estate would normally close. If there is an attorney representing the executor, I might be tempted to contact him or her, share your concerns, and try to get a clearer answer as to when you can expect closure.