U.S. States: New York: Chenango County
I have recently gotten on line and just found your request for info. In think I can help.
According to my records, Benjamin Elmar Allcott (b.5/30/1769 d.5/13/1859) had 13 children. Of these, my grgr grandmother, Electa, was #5 (b.10/4/1802 d.1891?). The #6 child was another Benjamin who only lived a few weeks (b.9/1804 d.10/1804). However, #1 child, Amon (b.10/28/1792 d.5/11/1883) had a son, Benjamin (b.12/17/1827) who married Polly R. Page in 1852. This may be your Benjamin. Our records also show that Benjamin & Polly had at least two children: Lavern J. b.1853 and Henry H. b.1855.
It's interesting that in Chenango Cty. my Electa had a daughter, Weltha (my great grandmother b.11/1/1831) who married Henry W.Phillips and in about 1859 settled on a farm in Delaware County, Iowa. Directly across the road from her was a farm purchased by her first cousin, Joseph B. Alcott (b.1835). He was the son of #2 child, Ariel Allcott (b.2/21/1795) and grandson of Benjamin Elmar. Since your Benjamin, my Weltha and Joseph would all be first cousins to each other, your Benjamin might very well have gone to Iowa too.