1870 Malcomb Co, MI (Town of Ray) Census [p41 #269]: Almira A BARTLETT 26 b NY; Herbert J 6; Robert H 2; Leah A 1; ch b MI
This tells me 3 things: 1. Almira is probably a widow [Henry d 1865] [or there is a mistake in the census and John is just not listed] 2. Herbert was born c1864 [this would be consistent with being a "baby" in an 1865 letter; and would predate any marriage in 1866] 3. If Henry d 1865 in the CivWar, she's had two more children since, which were not his.
1880 Branch Co, MI (Girard) Census [p632D #334]: John G BARTLETT 47 Farmer b NY par b VT/VT; Almira A 36 wife b NY par b NY/NY; Herbert J 16 son; Robert H 12 son; Leah A 11 dau; Orlin A 9 son; Katie B 1 dau; Helen 1m dau; ch b MI par b NY/NY
[NOTE: #333 (next door) Alfred I NORTON 30 ... Jasper E ELDRED 36 Boarder b MI par b NY/NY - perhaps related to Almira?]
This indicates: 1. John G BARTLETT did marry Almira, probably after 1870... 2. John basically said all the children were his [unless Almira was the one talking to the Census Taker, and she didn't mention that one or three were his step-children - I've seen instances before where the relationships were clearly not from the perspective of the HOH...] 3. It looks to me like Orlina b 1871 may have also been born to Almira before she married John; and that they probably married c1878, and began having children together - do you have a marriage record for John G?
There is a John BARTLETT 37 NY in 1870 MI Census with wife Sarah 35 and 5 children... did they divorce and Sarah took the children?
As for the cemetery register: 5 Jan 1865 minus 24y6m28d results in a b 8 Jun 1840, which is in line with the info you posted for Charles.
It would be fascinating to me to compare the DNA of a male BARTLETT descendant of Herbert, of Robert or Orlin and any son by John & Almira.
Do you have the ancestry back from Henry and John?It looks like they were from VT - we do have DNA on file from a VT BARTLETT line...