Help IDing mini-widespread faucet cartridge
 

Hi,
I learned a lot two years ago about bathroom cartridges for sink, tub and shower faucet handles when all of them (Moen) pooped out within a few weeks of one another.

Now my problem is identifying the cartridge from my mini-widespread sink faucet handle for the pedestal sink in my powder room.
-I haven't been able to identify the manufacturer, but looks like American Standard (?)
-I removed the cartridge and took it to the "Big Box" store for assistance finding replacement(s). They weren't sure either, so I bought their three stem recommendations to try (of which, none seem long enough):
--Danco stock # 15624B hot/cold stem 31-11 H/C for Price Pfister
--Danco stock # 15625B hot/cold stem 2H-1H/C for Price Pfister
--Danco stock # 17216B hot/colc stem 4H-1H/C for Price Pfister
All of the above called for #8 size O rings, so I got a package of them, too.

I'm attaching photos of the sink, faucet external and internal pieces, from which I hope someone can help me identify the faucet manufacturer/make/model so I can learn what stem or cartridge (are they the same thing?) I need to replace. The bottom of the cartridge I removed, which sort of looks like a copper color, has a "nub" in the center--should there be a washer or O-ring resting there (where the cartridge meets the inside of the faucet)?
Extremely grateful for your insight, comments or recommendations!