Am I correct that if you make 4 z1 tube journeys in a day, then take the train from Farringdon to Gatwick, you will pay the z1-z2 cap + the cost of a single fare from Z1 NR to Gatwick?
What about if you made 3 z1 tube journeys, then travelled from Bank to Gatwick?
From what I can see a Z1 LU to Gatwick journey is priced the same as a Z1 LU journey plus the NR Z1 to Gatwick fare, so it seems that you should be charged £9.50/£17.50 off-peak/peak, plus the £8.10 z1-z2 cap, not the £12.20/£20.30 LU to Gatwick fare plus the z1-22 cap.
When you switch from one cap (zones 1-2) to a further out one (Gatwick) then the journey that takes you there will be charged in full, until you reach the new cap.
It is just possible that in the second case (Underground and Thameslink journey) the back office calculation might recognise that the Underground part ought to be treated as part of the cap. If this happens then contactless will charge the rail only fare straight away, while Oyster will queue an adjustment to be credited back the next time you use the card, but only if it’s a normal adult card. The reason I can’t say for certain is that the extension fares charged by GTR have been fiddled to avoid an unintended consequence of the really cheap fare between East Croydon and Gatwick Airport. If you have the time then it’s always worth stepping back a train at East Croydon so you can touch out and back in again and split the journey into two journeys.