HUZZAH!It is free!
This is one of those situations where it seemed as if I tried every option the wrong way at the wrong time. Hm. Sounds like racing.
I ended up using brute force. Not a hammer, but a propane torch. Pressure in the area behind the shaft built up, forcing the errant piece out. A little WD-40 helped the process.
Step TwoDoes anyone have one of these (expletive deleted) pieces they would be willing to sell me?
It is a standard 750 F1 item as far as I can tell. Surprisingly, I can find no images of it online, so I do not know for certain.
Head: 19.5mm diameter
Lip: 3mm thick
Inner diameter: 16mm
Shaft: appx. 8mm thick (maybe 7.75-ish mm)
Overall length including head: 31mm
Alternately, I could do with a replacement pushrod and clutch center if it fits.
I am still wondering why it broke.
Odd, that.