I’m sorry if it sounds like a circular argument. If you are unhappy with the fares offered by the ticket machine at Rye House then I suggest you contact Greater Anglia and ask them to explain. They set both fares for paper tickets and the PAYG fares.
Sadly it isn’t technically possible to have fare extensions on 60+ Oysters or Freedom Passes. The reason is the different rules for different train companies. A touch in at Cheshunt and a touch out at Liverpool Street does not tell the system whether you used London Overground or Greater Anglia. There are numerous other examples as well.