It may be possible to confirm family relationships by comparing test results with Gregory or other carriers of his ancestors' Y-chromosome or mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree:
Family Tree DNA Y-DNA Test 700 markers, haplogroup I-FT85299, FTDNA kit #IN79110
Mitochondrial DNA test-takers in the direct maternal line:
Family Tree DNA mtDNA Test Full Sequence, haplogroup U5b2a2b, FTDNA kit #IN79110