While the coins on the eyes figure into the folklore of death as you've identified with the connection to Charon, they served the real purpose of being the right diameter and weight to hold the eyelids closed until the delicate tissues and muscles could fix into place. Suturing wasn't an acceptable option to close the eyelids; other methods are used in modern funeral service to avoid the problem of open eyelids. Many people are very familiar with the folklore without any knowledge of the practical application.
As to the employment of embalming surgeons, they were private citizens/contractors who followed the progress of battle until quite late in the War. In our case, we don't wear military uniforms. The trousers are dark green, and yes, the waistcoat is a high button military one; you've got me there. I bought them on sutler row at an event because I ran out of time needed to make them myself as I did with the rest of the wardrobe. I knew that we could dare to appear without sack coats (in progress) but that we dare not appear in public without waistcoats. Mine has hand-sewn buttonholes and details quite different from others that the sutler had for sale. I recognized the high quality of the garment; so I bought it with the intention of later adjustment. I haven't been able to bear ripping the brass buttons off of it, and I haven't found buttons that would be correct. I may make my own to correct that detail. I've also acquired a grey civilian waistcoat with lapels and fabric-covered buttons. I've concluded that if asked and in the navy one, I'm wearing a dead officer's waistcoat taken in payment for services.
I haven't taken photos of our instruments and chemical display. Admittedly, they are basic. I'll try to take photos at our next set-up.
I remain as ever, your faithful & obedient servant,
aka Benjamin Franklin Lyford, M.D.
Drs. Chamberlain & Lyford, Principal Embalming Surgeons
Washington City, D. C.
Adservio mortuus quidnam es non potens adservio ipsum
Traveling with while in the field:
Mid-States Living History Association, Indianapolis, IN
10th Illinois Cavalry Regiment, Springfield, IL
The Society of Civil War Surgeons