Thanks to Cynthia Villa in Utah for DNA confirmation via AncestryDNA in October 2018 and providing additional information. Cynthia is a descendant of Alice's brother Thomas Briggs.
Marriage source:
"England, Manchester, Parish Registers, 1603-1910," database with images, FamilySearch (
https://familysearch.org/ark:/61903/1:1:FMRM-899 : 17 December 2015), James Crompton and Alice Briggs, 12 Jul 1796, Marriage; citing St Mary, Prestwich, Lancashire, England, Archives Central Library, Manchester; FHL microfilm 2,356,184.
Possibility of Alice Barns m 30 Aug 1795 - now discounted:
England, Manchester, Parish Registers, 1603-1910," database with images, FamilySearch (
https://familysearch.org/ark:/61903/1:1:FMRM-C9K : 17 December 2015), James Crompton and Alice Barns, 30 Aug 1795, Marriage; citing St Mary, Prestwich, Lancashire, England, Archives Central Library, Manchester; FHL microfilm 2,356,184.