Hi Graham,
Sadly this is a case of different policies combining to make things difficult. Greater Anglia, like several other companies, allow contra-peak travel in the afternoon to be at off-peak rate. As soon as you want to include Underground or DLR travel then it becomes peak for the whole journey. There is no differentiation between Central London and a bit further out.
Where interchange involves passing through two gatelines the system automatically joins legs into one journey, which is normally what you want, but not always. An unfortunate case at Tottenham Hale is that the interchange time is set to 20 minutes, which is completely over the top given how far apart the gatelines are. If it was only 5 minutes then it wouldn’t be too onerous to wait and cause the two legs to be treated as two journeys.
You have a few options. You could buy a ticket for the Greater Anglia leg which should be at the off-peak rate, then use contactless for the Underground. You could also use two different cards, if available, but beware that capping won’t apply properly if you were later to go into Central London. If you don’t mind paying an extra £1.75 then you could touch in on a bus at Tottenham Hale and get straight back off. Bus drivers are quite used to this so won’t bat an eyelid. The effect of the bus journey breaks the interchange immediately. Finally you could intend to do something else for 20 minutes and let the interchange time out naturally.
I do sympathise with your situation, and hope that one day a sensible policy will be applied to fares, but for now this is how it is.