Your search sounds very similar to my missing paternal grandfather for whom I have located a scant four records. But I digress!!
When Rhoda married at age 24, could it have been a second marriage and thus Ingram was not her maiden name? It sounds like you are assuming that she was born in the U.S. and always lived in Wayne County. In the 1870 census I see a Rhoda Ingram living in New York state with parents and siblings, and she was born in Canada. You might pursue that family, since she has a similar birth year.
What I read suggests that you have relied quite a bit on internet searches. Everything is not on the internet. Just because a death record does not appear on Seeking Michigan does not "necessarily" mean that no record exists. It will cost a bit, but I would suggest seeking a death record from the Wayne County Clerk's office for the years 1885 to 1897 which you suggest. While the search might turn up nothing for your money, at least you will know that you have attempted that search.
You might also look in the Detroit City directories for Rhoda Ingram in case she was living alone for some years during the times you noted. Once again, for a little bit of money I would pay for a death record for the Rhoda who died in 1936 in Garden City. Don't assume anything!! Check all the records that might reasonably be your lady.
Good luck in your search.
P.S. We are not related!!!!