I finally found time to get this done.
Following the great advice here, I disassembled the rifle, and soaked everything down.... from the nipple, to the bore, and on. It was due for a good cleaning anyhow... no rust, but a fair share of dust.
I also discovered that my memory didn't serve too well at all. It's a Parker Hale Enfield 1858, two band, .58 cal.. I was close, but nothing about it was Navy Arms.
Anyhow, not having a bullet puller of that type, I decided to use the air hose trick. It worked great, and for anyone curious of what it took, or what it looked like..... once I acquired enough of a seal at the nipple end with a typical air nozzle and 110 lbs of air pressure, the bullet flew about 10' out in to my yard. Nothing too spectacular to see.
So I finished up by cleaning the bore as best as I could with a 12Ga bore mop, and then the rest of the exterior surfaces. I don't know how to remove the barrel, but I believe any damage that may have been occurring, if any, has been stopped for now. Plenty of Rem-oil was used.
I couldn't get enough light in there to see if there was any damage to the back of the bore, but nothing but unburnt powder showed up on the bore mop.
No matter. I have no use for the gun, and will likely hang it on the wall or something, now that I know it isn't a bomb waiting to be ignited.
Thanks so much for the help. My hat is off.