The book REMINGTON ARMY and NAVY PISTOLS 1861-1888 by Don Ware has the info you are looking for. Unfortunately I do not have a copy.
From my notes, the highest serial number New Model Army accepted by the US Government prior to the end of the Civil War on April 9, 1865, is 148550. It was part of a shipment accepted in March 1865, and I doubt this gun would have been issued before the end of the war.
Also from my notes, NM ARMY #81728 accepted June 1864, #92603 accepted June 1864,
#12603 accepted December 1864. I think these might have been issued before the end of the war. Hope this helps.
Regards,
Powderman