Thanks Toolmaker 51 & Marv for pitching in.

Long story short:
My hindsight always has 20-20 vision, and I really should've stayed off trying to correct the vial's position within the tube...
"I'll just" was the inspired thought of the moment last night, by dissolving the fixing cement with an acetal acid solution,
carefully working the vial tube free to refit in its intended, proper place.
The flat, short end of the vial worked like a charm, (yup - you all already know what'll come...),
and the other deeply set, molten neck end showed promising results, just 'til I heard a small crack and felt a chemical smell...
-Any of you guys having tips on how to refill and seal a vial with a broken-off tip?

It really is a bit like gambling - each time you run the high risk of ruining everything in pursuit of "just fixing" that tiny fault.
Oh well, apparently at least ONE of us HMT posters can't be instantly successful each and every time, right?

I'm not sniveling (nor asking for pity or compassion), but it seems like my very first entry here:
Repeat Reading Gage - DIYSwede's "Cheap-O-Meter"
were the best (so far) - I've just gone downhill from there...

The everyday trudgery of a cheapskate machinist is a blessing in disguise, so I'll be back.