I think it is very likely that your Roman Loomis Agard was a nephew of James S. Agard whom I am searching.
I assume you have seen the History of Medina Co., OH (Chicago: Baskin & Battey, 1881), p443 which mentions Roman, his brother Alvin & their father Benjamin. Although it says the two sons were born in Colbrook, CT, I have found instead that they were born in Torrington, CT.
Barbour Collection, CT Vital Records - Torrington Benjamin Agard m Rhoda Loomis, 7 Apr 1796 Alvin Agard, b 14 Jan 1797 Aurelia Agard, b 6 Mch 1799 Rhoda Agard, b 23 July 1802 Roman Loomis Agard, b 3 Dec 1804
Contrary to what it says in the History of Medina County, I have found no evidence that Benjamin Agard might have been born on Long Island.
Benjamin & Rhoda Agard are in Torrington, CT deeds as late as 24 Dec. 1806. They are in Portage Co., OH 1812-18 & in 1819 are in Medina Co., OH.
Rhoda Loomis' lineage is in The Descendants of Joseph Loomis by Elias Loomis (New Haven: Tuttle, Morehouse & Taylor, 1880).