I'm just listening to the commentary voice-over of the first season of Dead Like Me and noticed that Ellen Muth who is from Connecticut from time to time uses t-glottalization! That's so amazing! At that time on the set of Dead Like Me she has been working with Callum Blue who (at least there) uses consistent t-glottalization. Also the Wikipedia article says that even "Prince Harry frequently glottals his Ts". I can absolutely understand why that's so contagious. ;-)
By the way, yarb, Dead Like Me was shot in Vancouver, BC.
I'm not a native speaker of course but my natural way of pronouncing "button" is to obstruct (or rather completely stop) the airflow at and around the alveolar ridge like when pronouncing /n/ from right after the /ʌ/ onwards which renders the rest of the word nasal, and I think there is also something glottal going on. When I pronounce it the way Ellen does—the Cockneyesque way—the airflow isn't obstructed on the height of the alveolar ridge until the /n/. (It is of course for the /b/ with the lips and then in the glottis.)
There is a transcription of someone from Mississippi here, who used a lot of glottalization, too. It isn't as special as it seemed to me at first, I guess. I'll probably try and add a few glottal ts to my speech if I should happen to have mental resources to spare. ^^
There is something in this Mississippi business. Previously, you said there's elision in word-final /t/ generally and real glottal stops in words like 'button', which I would agree with. However, in the mp3 you provided, the speaker truncates word-final voiceless stops to such an extent that they really sound like glottal stops.
The other interesting aspect of the accent is that non-alveolar stops are truncated just as much as /t/, whereas (according to my ear) in General American the /t/ sounds more 'cut down' than the others.
In Ellen Muth's speech I can hear basically all varieties: with the usual alveolar flap, with the seemingly elided t and with pretty pronounced glottal stops. Something I should be listening out for once I have time is when the ts are pre-vocalic and when not and what bearing that has on their pronunciation.
The paper focuses on word-final pre-vocalic glottal stops, so the button phenomenon (phonemenon) probably won't be explained.
Darn, now I have to go to the next lecture...
There is a Wikipedia article that seems quite interesting, but I don't know how viable it is to try and apply that to American English.
I quickly listened to short sequences of Ellen Muth in of "The Young Girl and the Monsoon" (1999) and though there wasn't much time, I think I heard a few glottal stops at word-final pre-vocalic position.