Sorry for the trouble this is causing! Things are meant to work as you describe, so don't give up hope yet. :-)
When I added a new single-action list to my database, then put nine items on the list, I was able to switch between Remaining, Available, and Next Action availability filters and see all the items in all three cases.
That said, I didn't add any start dates, due dates, or even contexts to those single action items - maybe one of those fields are the reason why your project is behaving differently than mine?
Our support folks have headed home for the evening, but if you send an
email or call 800.315.6664 in the morning, they'll be happy to help sort this out. Sorry again for the trouble!