Hello David,
I am glad you are excited about your Parker and are shooting it! I attached pictures of one of my Parkers with a serial# in the 9000's. It is a grade 0, 10 gauge with Stub Twist barrels. The stocks are not checkered, though there is a medallion. This is what your gun probably looked like when new back in 1875. If yours did originally have a pistol grip stock(which may be possible) it would likely not be checkered and have a different shape.
There should be a medallion behind the hammers/tang regardless of stock configuration. I have Parker# 1219 and it has the medallion. By the way the bottom picture you mentioned by TXhuntermn(Mark) without the medallions on the tang are not all Parkers. He just has alot of awesome hammer guns
At some point someone cared enough to fix your gun or replace the stock so they could keep on using it. It might take away from the value, but not the character. I would buy another firing pin and keep on enjoying it.