Maybe I’ve just not been keeping my eyes open, but I can’t recall reading any surveys of the prevalence or otherwise of what I would like to call nt-reduction.
One resource I overlooked has now been brought to my attention by Kensuke Nanjo, phonetics editor of the Genius English-Japanese Dictionary, Fourth Edition (2006), in a long email which is worth quoting in extenso. He claims that this “G4” is
the only dictionary that distinguishes [nd] (t-voicing) and [n] (t-deletion) for underlying /nt/ in American English. G4 gives [nd] for carpenter, certainty, into, ninety, seventy, Washington as their second variant in American English while it shows variants without /t/ for other /nt/-words like center, dental, Internet, plenty, twenty, winter, etc. with the label "casual AmE".
Kensuke says that the decisions he made were
based on some books and papers that I'd read and personal communications with American phoneticians, perhaps including the late Becky Dauer, but I'm afraid I don't very well remember where I obtained the data. This distinction ([nd] vs. [n] for /nt/), however, is mentioned in the phonetics/phonology chapter I wrote for the book Ando & Sawada (eds.) English Linguistics: An Introduction (2001), so I obtained the data more than a decade ago.He further comments
You rightly mention that "it does not happen in the environment of a following stressed vowel, as in intend, contain", but both LPD and G4 record /nt/-reduction for Antarctic, perhaps as a sole (?) exception.— probably because of the transparent morphology which makes ant#arctic seem like a compound comparable to print#out, in which nt-reducers do reduce nt.
Also, I agree with your comment that "[it doesn't] apply to ntr clusters, as in country. The t can be lost in centre/center but not in central", but G4 gives the variants like "inner"-duce and "inner"-duction for introduce and introduction respectively, with the label "casual AmE". This is based on my own daily observation about American English. Needless to say, this is a case of r-to-schwa metathesis, which triggers /nt/-reduction. In fact, I tried to include as many cases of common metathesis as possible in G4, so it gives the American casual pronunciation "hunnerd" for hundred, a case of both r-to-schwa metathesis and lexically restricted /nd/-reduction (e.g. can'idate, fun'amen'al, kin'a, un'erstand, won'erful).
These nd-reductions of casual speech are very relevant, too. Thanks, Kensuke.