Bill, That is a nice back action Parker. Most of the ones I have seen are rough and with the exception of the stock, yours is in good condition for a back action. Is the barrel steel printed on the rib of the barrel? That would give as an idea of grade and initial price in 1869-1870.
That may be a replacement stock as I don't believe I have seen a back action with a pistol grip stock. That is why it would be good know the barrel steel and if there is any engraving on the receiver. If it is a higher grade gun, the pistol grip stock may be original as it was the "new" cool thing at the time.
I really like the Parker back actions. You definitely have a gun I would try to get back in the field. I have a few of these and enjoy shooting them with black powder and light nitro loads.
Here are a few threads with info and pictures of back actions:
https://parkerguns.org/forums/showthread.php?t=28813
https://parkerguns.org/forums/showthread.php?t=38165
If you have any questions or you or need some help please let me know. And perhaps more importantly, I am not that far away in Rhode Island, and we could have a great day of Parker back action shooting!
Quick Edit I zoomed in on the barrel rib and could see that the barrels are Laminated Steel, which was for a higher grade...very nice!
Jay