first of all, thank you for listing what you have tried:
this.byId("__table0").getItems().length // this will only give you the visible number of items
A suggestion I have is to provide the table id yourself (so it is constant) instead of using the dynamic generated id (seems like you used it "__table0" because of possible changes in future releases may not guarantee the same pattern...
one thing you could do is to read the number of items from the odata service - I am assuming you are using an odata service - and that can be done with the odata url syntax as: URL/pathToEndPoint?$count and putting that to your label or value holder for number of items.
because it seems like when you navigate back and forth on the screen, the number may not be the same, correct?