I am a descendant of Amos Eldridge, b. abt. 1839, d. 1921, probably in Canandaigua, Ontario, NY. I have one census record in which Amos, wife Sarah and daughters Clara and Flora (my gr-great-grandmother) are living in Victor, Ontario, NY in 1880. Other than that, I have Civil War veterans records that corroborate the family relationship and year of death.
I have no information about Amos's parents except they are born in "England" which I assume could be English Canada. I stumbled across Ontario County indenture listings on raims.com for Amos, Mary and Theodore Eldridge between 1851 and 1855; and a 1950 census that lists Amos and John Eldridge, aged 13 and 9, among the population at the Ontario County Poorhouse in Hopewell, in 1850).
According to the the 1900 US Census of Ash, Monroe, Michigan, Amos Eldridge is living with sister Mary and her husband William Conkrite while Sarah appears to have stayed in Canandaigua living with her daughter Clara and son-in-law William Stevens. Both Amos and Sarah are still married, though Amos says it's 28 years and Sarah says it's 30.
There is an Amos Eldridge in Brasher, St. Lawrence County, NY whose year of birth is about 1828 according to the US Census for 1850. Also, an Amos Eldred born about 1844 in Middlesex, Yates, NY. I have ruled out either of these despite their proximity.
The Eldridge/Andrews family you've described may not be directly related but it would be a great help if you think you may have come across information relevant to my research.