Speaking as a real-life, recently successful, tube challenger :-), the answer is to use Oyster/contactless for the z7-9 bits and the GA smart/travelcard for the rest.
This is perfect if ending at Amersham/Chesham because there’s plenty of time to touch in and out. If starting at Amersham/Chesham then continue on Oyster/contactless to the first intended exit point within z1-6, typically North Harrow or Northwick Park. Costs a little more that way, but much cheaper than a weekly TC on Oyster/smartcard (which I’ve also used for the challenge).
In either case, just be aware of and keep an eye on, maximum jouney times; though a maximum fare would still be less than a weekly travelcard.