Update: it all works now!
I got just a little bit more packing material out using a flat 1/4 inch screwdriver. It felt pretty smooth and tight
in there, and as well as I could tell the resulting pocket was cylindrical with smooth firm walls, so I went on.
A tidbit I haven't seen elsewhere on the forum: the "packing gasket" people seem to be using is a Viton o-ring, ASTM size 102 (0.050 ID, 0.103 cross section, nominal 0.256 OD, all in inches.)
I hijacked a thin round-barreled cheap ballpoint as an insertion tool for the polystyrene retaining washer.
The ink tube fit nicely through the washer with little slop, the point served to center the tube in the already-seated o-ring, and the nose cone, drilled out to 1/8 and mounted backwards in the barrel, pushed the washer neatly into place. This is not as nice as the better versions from PenTooling/RZ or D. Nishimura but worked for this one-off task.
This morning (after the epoxy hardened on the retaining washer) I put everything back together without difficulty. The plunger pops back out if partially depressed as hoped, and the assembled pen fills nicely with ink.
Thanks for the help. I now have a nice late-'30s Lifetime Balance Autograph (and I even know the niece of the man whose signature is on the cap ring) for a total of $3: $1 estate sale price, $7 for head gasket/o-ring/retaining washer kit with a $5-off coupon from eBay. Other investments include a few milligrams each of silicone grease and plastic-welder epoxy (both on hand already) and a modified but still-usable OfficeDepot red ballpoint :-) Oh, and quite a few hours of pleasure figuring out what to do...