Alexander Bacon has offered the cash in a bizarre "photographic competition" he thinks will show Stone was 40 miles away when Lin, 45, and Megan, six, were bludgeoned to death in Chillenden, Kent, in 1996.
Dr Russell's older daughter Josie, then nine, survived the attack.
Stone, 48, was jailed for life for the murders in 1998 and, after his original conviction was quashed, was jailed for a second time in 2001. Dr Russell, who lives in North Wales, said he was dismayed but not surprised by the contest.
The appeal is has been set up on a website run by writer Bacon, of Sydenham, South London.
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