As you figured, the TimesheetViewQuery returns the relevant work items only, to be filled into a TimesheetQuery for example.
If you know the work items IDs you could use the TimesheetQuery directly (or the more general EntityQuery).
The TimesheetQuery is the one to use for your purpose (possibly following a TimesheetViewQuery).
However, you mentioned TimesheetQuery did not return the expected entities. This may be a permission issue. Timesheet entries retrieved through the API are according to the user's (logged into to the API) permissions.
To check for permissions, login to Clarizen with the same credentials and check if the expected entries are available there.
If you need access to all timesheet entries in the system, try using a super user's credentials.
If you think permissions is not the reason, I'll need specific information about the way you used TimesheetQuery (a code snippet is best) and what results were not returned.
Hope this helps.