Hello Katwoo,
Taking another look at your Woogate family, I wonder if the Francis Woodgate aged 2 years and 8 months - son of Clifton (Thomas) and Mary on the 1930 Census is :- John F Woodgate. The 1930 census was April 1930 so age would fit. Would also be another one to ask RAOGK volunteer about.

John F. Woodgate
Born 4 July 1927 and Died 1 st Nov 2007
Last Residence: 49783 Sault Sainte Marie, Chippewa, Michigan
SSN issued: Michigan (Before 1951)
Regards
Sandra