Sounds like the question is not going to count in the scoring for this month, but I went ahead and looked for an answer, anyway.
I found a number of sources indicating that 2,111 unknown Civil War soldiers were buried in a vault at Arlington National Cemetery (specifically, in Mrs. Lee's rose garden) during April 1866; however, the same sources indicate that number did not consist exclusively of Union soldiers, but included both Union and Confederate. I'll be interested in knowing whether that was the official answer, or whether there actually is a place where 2,111 unknown Union soldiers were buried that same month.