I don't know if "Zimri" is a nickname for "Zachery," sorry.I guess you would have to evaluate where you got the information that your William Allen Warren's father was named Zachery...was it William's death certificate, for example?
I found a couple more items on this Zimri Warren:
1880 census for Hendricks County, town of Coatesville, page 640C:
#389-402 Warren, Zimri white male 54 married day laborer Dispepsy [sickness/disability column] born Ind. father born KY mother born Tenn.
--Abigail white female 37 wife married Keeps house Ind. NJ NC
--Eddie white male 4 son single Ind. Ind. Ind.
Alden, Francis white male 3 stepson Ind. Ind. Ind.
#389-403 [same dwelling, different household]
Thompson, Mary white female 37 single Dressmaker O. PA. O.
1900 census for Hendricks County, Clay Township, page 158A:
#385-387 Warren, Joe head white male Dec 1853 age 46 married 15 years born IN father born IN mother born IN Labor, R.R. 3 months unemployed yes [can read] yes [can write] yes [speaks English] Rent -- House
--Maggie wife white female May 1854 age 56 married 15 years 3 children born 3 children living KY KY Germany
--Mark son white male Sept 1885 age 14 single IN IN KY Labor, day yes yes yes
--Bennie son white male Nov 1888 age 11 single IN IN KY at school 6 months in school yes yes yes
--Malhan son white male Feb 1892 age 8 single IN IN KY at school 6 months in school yes yes yes
from A Portrait and Biographical Record of Boone, Clinton and Hendricks Counties (1895):
Zimri Warren, of Coatsville, is one of the old soldiers of Hendricks county, Ind., whose father was a pioneer of Putnam county, where he entered land.Zimri was born Sept. 23,1825, in Bloomington, Ind., son of Drury and Elizabeth (Legg) Warren.He was reared a farmer and married Patsy, daughter of Benjamin and Lydia Robinson, and to Mr. and Mrs. Warren three children were born: Wesley, Joseph and William.This wife died, and Mr. Warren married Abigail, daughter of George and Elizabeth Layton, and to this marriage was born Eddie.In March of 1865, Mr. Warren enlisted, at Indianapolis, in company H, Eleventh Indiana infantry, for three years or during the war, and was honorably discharged at Baltimore, on account of the closing of the conflict, in September, of 1865, and after a service of seven months on guard duty at Baltimore he was mustered out.He was one of a detail to fire a salute of cannon in honor of Lee's surrender, and was made deaf from the noise of the discharge.Mr. Warren is a member of the John Layton post, G.A.R.
from The People's Guide: A Business, Political and Religious Directory of Hendricks Co., Ind. (1874):
Warren, Zimiri; boarding house; Coatsville.Born in Ind. 1824; settled in Hendricks County 1865.Republican, Protestant.
from The History of Hendricks County edited by John V. Hadley (1914):
p.532 [sketch on John W. Figg--I am abbreviating it here to include just the part that mentions Joseph Warren]
John W. Figg, the proper and efficient superintendent of the Plainfield schools, was born in Putnam county,Indiana, December 13, 1859.His parents were Robert P. and Abigal (Layton) Figg.His father was born in Kentucky in 1837 and came to Indiana with his parents, Mr. and Mrs. Francis (Asbury) Figg, in 1848 and settled in Putnam county.His mother came from Pennsylvania with her parents to Ohio and later the family settled in Putnam County, t his state, where she met Robert Figg.When the Civil War opened, Robert Figg enlisted, in December 1861, in the Sixty-second Regiment, Illinois Volunteer Infantry, and died in March, 1862, at the age of twenty-four, leaving his widow and three small children.John W. Figg, the leading subject of this sketch, was only three years of age at the time.The other two children were Elizabeth, who died at the age of twenty-two, leaving her husband, Joseph Warren, and one son, and Rebecca Olive, who married Myron Stanley.She died at the age of twenty-one, leaving one daughter, Elizabeth.
from The Republican (Danville, IN), issue of 11 March 1897--page 1, column 2:
Mrs. Zimri Warren died here very suddenly Saturday night.She had been in poor health for several years but had been as well as usual that day until evening.She was a member of the M.E. church and as long as health would permit she was quite a worker in church affairs.She leaves a husband and two sons and many friends to mourn her loss.
from The Republican (Danville, IN), issue of 23 June 1898--page 1, column 1:
On Wednesday evening Uncle Zimri Warren had a stroke of paralysis from which he died Friday morning.He was one of our old and much respected citizens. He was born Sept. 23rd, 1825, in Putnam county.He was twice married, his last wife being dead only a few years.In the spring of '65 he enlisted in the 11th Reg. Co. H. Ind. Vol. He leaves four boys, all of whom are grown.His remains were laid to rest in the cemetery east of town.