After a year of lobbying, we have just been informed by TfL that passengers can now purchase a Monthly ticket on Oyster directly from the ticket office or Ticket Vending Machines at the London Overground stations on the Sydenham line. No longer will you have to go to London Bridge or a station north of New Cross Gate.
If a passenger requires an Annual season ticket on Oyster however, they can request it from the station but it would have to be collected the following day (or later). TfL apologised if staff have been advising passengers to travel to another station as this is not the case and LOROL has confirmed that the staff have been re-briefed them so this should not happen again.
While not ideal, this is at least progress.