You *can* use the Family Search API even though they have no already written tools. This is suggested in the [link][1] Colin left in [his answer][2].

Specifically, someone has written [a python script][3] that exports to GEDCOM. Not sure how well that translates to a spreadsheet.


  [1]: http://support.legacyfamilytree.com/article/AA-00387/0/How-to-download-your-ancestors-from-FamilySearch-Family-Tree-into-Legacy.html
  [2]: https://genealogy.stackexchange.com/a/10573/6103
  [3]: https://github.com/Linekio/getmyancestors