Hi Jane
I looked for John and Mary Ballard several years ago, reaching dead-ends rather than a conclusion. John was not baptized in Winterslow [nor in Idmiston]. There is a death for Mary Ballard aged 90 registered for Alderbury in 1867, I assume she is ours.
There is only one earlier entry than Sophia for Ballard in Winterslow PR and that is Jenney in 1778 with parents George and Elizabeth. I have just tracked down the marriage of these two [I have also now found it in the IGI], which was in Idmiston between George Ballard of Winterslow and Elizabeth Goodfellow of Idmiston; Elizabeth probably lived in The Shripple in Winterslow, which is a detached part of the parish of Idmiston - if so, she was 37 at the time of her marriage. If John's burial is correct, these are not John's parents. There are no burials for Ballard in Winterslow or Idmiston up to 1837. The presence of George Ballard in Winterslow would explain why John turned up there.
The only possible marriages of a John Ballard to a Mary in the IGI are in Sussex, which at present seems unlikely. Ropley PR has not been extracted into the IGI, however, the PR is available on film, so I shall borrow it, but it will be at least a month before I get a chance to look at it.
I'll let you know what I find.
Best wishes
Colin