I was thinking about this as I typed yesterday and had the same questions that 1866yb and Tim raised as I was typing.
I have seen the plug that goes against the shaft referred to as both a fiber plug and a Bakelite plug in different GM manuals. I don't think that replacements are available, so that is why I suggested the nylon spacers. I don't like my idea of filling the spacer hole with JB Weld for the same reason mentioned in the above post. The link Tim posted has some good ideas for a replacement. I'd also consider a nylon spacer filled with regular epoxy, not JB Weld.
I took a closer look at the fitting that the grease cup screws into. It has a gasket (leather?) fitted to the end to keep grease from leaking out. So my thoughts about grease oozing out when tightened as a good thing are incorrect. The grease is oozing because the gasket is worn and needs to be replaced. Funny, I couldn't get grease to ooze out of the grease cup on the 235 in my '57. Now I'm glad it doesn't!
My apologies for any confusion,
Matt