Now I'm wondering what the longest Underground trip is without visiting a given line more than once. Probably needs a rule about the District and Circle lines where they overlap since you could get a lot of mileage out of that. (I calculated the shortest one that includes all lines back in the early 2000s but they've obviously changed things around since then.)
A route out to Epping via Newbury Park would be another option though, probably elephant/bank/kingx/green park/bond instead.