Chris – this may not help but it reflects my experience when looking into the same issue. I wanted to do a ‘Tube Challenge’ so needed a ‘go anywhere’ ticket. I didn’t buy the paper ticket. After a lot of research and advice from others I bought a Z1-6 Day Travelcard electronically & loaded it onto a Smart Card. I used Chiltern Railways but you can use other companies too. The only part of the Tube not included was the NW part of the Met line, and I used PAYG for that. During the day I tapped in and out of the tube, buses & overground, with no issues at all. From memory, last September, the TC cost under £15.