Dead here means utterly, absolutely, which is not a slang usage. Etymonline suggests that it hails from the 14th century, but does not explain whence it derived:
Used from 16c. in adj. sense of "utter, absolute, quite" (cf. dead drunk first attested 1590s; dead heat, 1796). As an adv., from late 14c. Dead on is 1889, from marksmanship.
I would guess the following: death -> permanence -> absoluteness. But this is all speculation. I doubt you'll ever find an authoritative history of this evolution.
The earliest Google Books match for an instance of doctored in a transitional (or perhaps post-transitional) sense between "amended" and "adulterated" appears in William Marshall, The Rural Economy of Glocestershire; Including Its Dairy: Together with the Dairy Management of North Wiltshire, and the Management of Orchards and Fruit Liquor, in Herefordshire, volume 2 (1789):
Men in general, however, whose palates are set to rough cider, consider the common sweet sort as an effeminate beverage; and rough cider, properly manufactured, is probably the most generous liquor; being deemed more wholesome, to habits in general, than sweet cider:—even when genuine. That which is drank, in the kingdom at large, is too frequently adulterated. The "ciderman" cannot afford to lose a hogshead: if it will not do, it must be "doctored": or if sound, it may not be sweet enough for the palate of his customers; nor high enough coloured to please the eye; but the requisite colour and sweetness, he finds, are easily communicated.
This is evidently the sense of "doctored" that appears as OED definition 3 in tchrist's answer:
3. fig. To treat so as to alter the appearance, flavour, or character of; to disguise, falsify, tamper with, adulterate, sophisticate, ‘cook’.
And yet it is not so very distant from the OED's definition 2b (again as quoted in tchrist's answer):
2b. transf. To repair, patch up, set to rights.
The line between "repair, patch up, set to rights" and "disguise, falsify, tamper with, adulterate" is not clearly demarcated—certainly not if you are a ciderman stuck with a hogshead of cider that no one will buy in its present state. Rather, it's a continuum that begins innocently enough with making improvements that are to everyone's advantage, and only gradually gives way to disguising an inferior product without acknowledging its original shortcomings or—in the worst case—without actually improving it at all. In this respect, it mimics the difference between sound medicine at one end of the continuum and quackery at the other.
Best Answer
The phrase take Manhattan appears to reference the song Manhattan by Rogers & Hart, first heard in the Garrick Gaieties from 1925.
The line in the original is We'll have Manhattan, the Bronx and Staten Island too ... [lorenzhart.org]
Later renditions changed that line (among others) to I'll take Manhattan, ... [spiritofsinatra.com]
It also has overtones of the military meaning of take
The phrase, I'll take Manhattan ... has become a meme, giving rise to a number of other works, as discussed by the original poster.