'Ain't'

The Dictionary feature on my Macbook, based on the New Oxford American Dictionary, 2nd Edition, defines 'ain't' as (non-italicized brackets represent my own input, italicized represent those of the NOAD):

informal: contraction of
-am not; are not; is not [thus, a construction of 'to not be']: 'if it ain't broke, don't fix it'
[ORIGIN: Originally representing London dialect]
-has not; have not [thus, a construction of 'to not have']: 'they ain't got nothing to say'
[ORIGIN: from dialect 'hain't'.]
+/-

The question this brings up in my mind is, of course, how in the world do we get the bastardized 'ain't' from am not (I'm not, or amn't?), are not (ooh! aren't!), and is not (isn't)? Worse yet, how do we arrive at a negative syntax construction from a negative contraction (hain't)? I can see how 'hain't' evolved into 'ain't' from the Brit dialect, fond of dropping H's ("'is 'ouse is 'appy coz 'is woif 'as 'it the roade") but how a contraction of 'has not' or 'have not' (usually followed by 'anything,' as in 'they havn't anything to say,' or 'they hain't anything to say') baffles me.
Or, rather, it used to, but I think I've the solution.

Look at the vast majority of speech in the US dialects of English. We're fond of the redundant colloquial construction 'have got' but use it improperly. Take the sentence 'I've got to shop,' for example. The extended form of the sentence is 'I have got to shop.' 'Got' in normal usage refers to the preterite form of 'to have,' i.e. 'I got the flu.' Thus, the proper form of 'to have + to get' is in the past participle, i.e. 'I have gotten (i've gotten) sick before.'
The main reason for using it in the present-tense construction of 'I have + infinitive' is because 'have' lacks a full stop consonant like t. Speakers can put more emphasis on their plight with that hard stop: 'I've got to get this assignment done' can be more emphatically and powerfully delivered than 'I have to get this assignment done.' It also aspirates less, so the chances of blowing your audience away with your Phelps like lungs (toke, suckah!) is minimized. Making the 'have got' construction is as easy as adding a one-word negative after the got: 'I've got no time,' 'I've got nothing to do.' It easily follows the positive contraction's rules for changing to negative, though no more so than the previously-stated-to-be-correct have + infinitive.

Since 'hain't' is a dialectical shift of 'hasn't' or 'haven't' and a modernizing shift from archaic 'ha'en't,' it's easy to see why this changes. However, 'hain't' is a negative contraction - the adding of 'got + negative' makes a double negative, when the word following 'hain't,' as with all negative contractions, must be positive: 'I hain't anything to do today,' rather than 'I hain't nothing to do today.'

Suffice to say, 'have got' (and its brethren) and 'ain't' (as a bastard child of other contractions) are on my shit list. [...]