How do Americans pronounce the 't' in "romantic", "countable", etc?

As for a 't' trapped between /n/ and a vowel, I've heard it pronounced in three different ways:

Maybe the formal, standard way is to fully pronounce the /t/ sound:

romantic: /roʊˈmæntɪk/

Another way is to omit the /t/ altogether:

Atlantic: /ətˈlæn^(t)ɪk/

Yet another way is to pronounce it as a flap t (represented here by the letter τ):

countable: /ˈkaʊnτəbəl/

These are how the Longman Dictionary on my computer articulates these words; romantic with a clear /t/, Atlantic without a /t/, and countable with a flap t (shown as /τ/ above), while all these words have a /t/ in their phonemic transcriptions.

So what's going on? Are there any rules as to when you should follow each pattern?

My intuition is that these three pronunciations are in free variation, so there is no morphophonemic rule that can help you decide when to use which. The first, where /n/ and /t/ are both pronounced you can call a "recitation" form, and you would use it, for example, when dictating a message over telephone or speaking to a foreigner who has trouble hearing English.

The other two are gotten by two common rules of reduction. First is assimilation of the nasal and plosive consonant (t not pronounced). Second is loss of the nasal consonant and nasalization of the vowel. Unstressed /t/ preceding a vowel may be flapped, so that's why you get the flap pronunciation.

The possible loss of n before t is important for these words. Nasal consonants are lost before voiceless stops at the same place of articulation in many dialects of English. This happens after the nasal has made the preceding vowel nasalized.

If the n before t remains, then so does the t. But once the n is lost, in American English the t is subject to flapping, which only happens intervocalically. That is, the loss of the n brings the t into contact with the preceding vowel, which makes it possible to flap the t.

The flap that results from flapping the t is a sonorant (like the vowels, nasals, and liquids) and is subject to nasalization by an immediately preceding nasal sound, so since the preceding vowel is nasal, this makes the flap nasal, as well.

An intervocalic n is also subject to the flapping process, which makes it into a nasal flap, in effect merging the pronunciation of intervocalic nt and n, so "romantic" and "Romanic" (if there is such a word) may come out sounding the same, both having a nasal flap.