The call/read REST calls are only available in (alpha) 6.2 PBX images at the moment which is why you are getting a 404 in your 6.1 image. Sorry for the inconvenience.
An alternative way of doing this with any PBX post 4.1 is just to pull the billing data for a date range:
The cookie that needs to be saved is called "Red60urne". The response will include a redirect "Location:" header, but this can be ignored. You should use HTTPS if you have a certificate installed.
A query that should get you all OUTBOUND calls for all phones in CSV format:
NOTE: The above URL provides a redirect "Location:" header. It is necessary to follow this redirect once to get the data. If that is a problem, you can look at the destination, and emulate it directly, but that interface is not guaranteed to remain consistent.
3) INBOUND CALLS
From version 4.1 of the PABX software you can specify "allext=1" to request a report for all inbound extensions.
The date range can be specified using:
month=&bill_start=yyyy-mm-dd hh:mm&bill_end=yyyy-mm-dd hh:mm
But due to memory and complexity constraints, the maximum report period is 45 days.
Also note that with CSV reports, new fields will only ever be added to the end of a line, so it is probably best to assume extra columns can be ignored for future-proofing.