Hi Colin,
I added a comment to a post on Nextdoor about this very query, though I can’t now find it. Was it you asking originally?
Looking at your questions, have you tried the fare finder on this site? That tells you which zones are covered for every Oyster journey (and some older contactless only ones too). Within zones 1-9 there are a number of fare scales, although only 3 relate to journeys south of the river. Overground is counted as National Rail if the whole journey is on National Rail, but it’s also counted as TfL if the whole journey is on TfL operated routes (or those like c2c which use Underground fares). The late adopting NR routes (Jan 2010) charge their own scale if any of the journey is one one of those routes. Additionally there is a mixed mode premium charged on top of the NR rate if the journey goes into zone 1, whether or not the TfL bit was in zone 1 or not. The Elizabeth line is more complicated. The core section between Paddington and Abbey Wood is treated like a tube line when combined with older NR routes, but the bits to Brentwood and West Drayton are also National Rail.
So, Plumstead to Greenwich to Lewisham is the same fare as Plumstead to Lewisham via Blackheath. When you start at Brixton LU you are already on LU and to get to Plumstead is defined as going through zone 1. It is possible to avoid zone 1 (Brixton – Stockwell – Clapham North (walk) Clapham High Street – Peckham Rye – Lewisham – Plumstead) but I guess that is deemed too many changes so no-one would do it. From Brixton NR you can go Brixton – Kent House (walk) Clock House – Lewisham – Plumstead, and I think that is likely to be the default route.