Jon,
Welcome aboard. While the Remington Society of America is able to assist in answering some of your questions, we do not have records on where or to whom a firearm was issued once it was accepted by the U.S. Government and/or left the Remington factory.
The presence of the cartouche (stamping) on the grip (handguard) indicates final acceptance by the U. S. Government Inspector on site at Remington. The cartouche "BH" is attributed to Benjamin Harris, a principal sub-inspector for the Ordnance Department.
The fact that two serial numbers are used normally indicates that there was a barrel change sometime during the life of the revolver. If you remove the trigger guard, the front tang will bear a serial number as well. Both serial numbers 75102 and 75580 would fall into the manufacturing date range of May 1864, and deliveries made that month were part of the contract of November 21, 1863 for New Model Army Revolvers.
That's all of the information I can supply,
Hope it helps,
Mike Strietbeck