You've done most of what you can do. The suggestion to get the Death Certificate is good, though Death Certificates are a gamble as to quality of info..depends on who provided it. In any case, you need it.
As to the missing father's line, I thought you had one possibility, though the man who died was in Marshall I think you said. Still a possibility...maybe he worked on trains or was a 'teamster' driving wagons and thus was in the area.
I did have that exact scenario and was just reminded of it in the case of my mother's great grandmother Louisa "Lula" Jane COIN (Cowen)(b1844 AR Indian Terr) BOLIN WASHBURN etc marriages who had a son Robert E. WASHBURN during the Civil War in MO. Seth E. WASHBURN who was from NY but living in IL with parents, joined the Union and was in Springfield MO area. After years of searching for the WASHBURN father, records were finally available for her divorce from BOLIN and her WASHBURN marriage (after the war, maybe late filing) and then a same-day 'bigamy' charge by the court again Seth. I ordered the Court records through the Christian Co MO library, but what I rec'd was not complete, saying only that he was already married to a BOLEN (very confusing) so don't know the outcome of his Bigamy charge (was he jailed?), but by 1870, Seth was apparently working his way back to IL and I found him in IA.
Then I found IL history on a site that had a short bio...talked about him hiring back on with the Army as a Teamster...based in Springfield so he was back in the area in 1870s and may have been present off and on in the life of Louisa & their son...though she had remarried to Liberty Hall McLAUGHLIN by 1871. However, Louisa had a curious marriage history and McLAUGHLIN seems to have left her high and dry before 1880, left MO and married again. Researching them has been interesting to say the least.
Louisa's father James COIN was a well-known wagon maker and blacksmith and I'm betting, from what long-time resident researchers told me, that he took care of the Military equipment, because he had himself set up at a crossroads on their route. This family does link with my AR famiy. Louisa's son Rob't E. WASHBURN (became a musician / composer in St Louis and remarried) had a son Robert E.L. WASHBURN b 1897 who mar Audrey McLAIN 1919 in Newport, Jackson Co AR (my grandparents).
What I have not done is try to get Seth's descendants to Family Finder test to see if we come up with some common cousin matches. The WASHBURN family (his father was a well-known physician) were well off and descended from old lines in the Northeast. I found one person with him in their tree. Seth's descendants did not have a clue that young Seth had fathered a child in MO. He married later on in IL, claiming on census that he had only 1 marriage, so I have no real proof other than the marriage record and court record.
I agree that the cousin-matching DNA tests and the results are hard to work with, and it is annoying to not hear from some of the matches. However, where there are 2 people who have some of the same matches, it is a very good indication of a match, even if the people who match are a man and a woman with different surnames. Often the reason we don't find our connections to our matches is because of what we DON'T know about our history. Thus I follow / track the lines of siblings on direct lines to see who they married and where they went. I may be a cousin to somebody because that person is related to Joe and I'm related to his sister Mary or brother John.
And I have my hands full. My mother and my spouse share multiple common cousin matches. I find how some are kin to my spouse, but have yet to discover how the match is kin to my mother. Old lines, paths crossed multiple times apparently.
Get that death certificate and see if there is a clue.