IIRC your rail journeys in peak time will be calculated separately from your off peak cap if you’re using contactless at least, so when you get to Amersham you should be capped at more than £14.9 but hopefully less than £21.2.
As for Oyster, I’m not sure whether such separate calculations exist on the day, or whether you have reached £14.9 in z1-6 before heading to Amersham, I think instead of capping less than £21.2 you will be capped at that price and then get a refund afterwards. But Mike should enlighten us.
Happy Easter!