Hi Ian,
Regarding one-piece (monoque) cases- thank goodness that by and large, Seiko historically chose to use one-piece stems that had an excess point to the set lever for removal of the stem from the dial side, so that this clumsy two-peice stem system was not widely employed in their one-piece cases (though there are some exceptions). Diatribe out of the way. I don't have any first-hand experience with the Cosmic in question, but I do have experience with, and understand the principles of two-piece stems. Here are some general answers:

1) The "fist" or male end of the inner stem that you describe has an interference fit with the "split" or female end of the outside stem portion. Once these are pushed together, there should be enough tension from the female portion around the male portion to keep the two piece together when the crown is pulled out using normal force.

2) the crown is removed two ways typically in a two-piece arrangement: a) excessive force is used to pull the outside stem off of the inner stem and/or b) with the crystal removed so that the movement can drop out of the case and the case held dial down, the stem is slowly rotated so that the split is parallel with gravity's force and the movement can drop out of the case. I like the second method better as there is less chance of damaging components during the use of excessive (but controlled) force. "b" is not always possible though if the design of the male and female ends does not allow them to slip past each other laterally, or if the movement is held in the case by some additional means (clamps, screws, etc that must be rotated correctly to allow the movement to be free of the case). In which case you must resort to "a".

It sounds like your stem components are worn out and should be replaced (you also mentioned them being in "poor condition"). This is common with two-piece stems that are old, rusted, or have been damaged from frequent use/abuse during dis-assembly and reassembly.


Here is a good, informative photo tutorial of uncasing a seamaster cosmic: http://www.old-omegas.com/tool107.html

 

Thanks Noah, your clear explanation is much appreciated. It seems like a pretty dodgy system for retaining a crown, but I guess when access to internals is through the crystal there are not a lot of options.
My case requires the movement to be rotated a few minutes anti-clockwise to allow it to drop out, so I will need to use method "a".
Now I can replace both stem parts knowing that I can still get back into the case.
I bought my son an auto Seamaster Cosmic for his 21st last year, and it sparked my interest, so I bought myself a non-auto that needs work.
Thanks
Ian D