Although charters can be rewritten, one problem is that most of the colonial charters specifically forbade titles of nobility. Only New York and the Carolinas did not.
It's hard to see how this could come out of the same conflicts that led to the ARW. Parliament isn't going to stand for a separate House of Lords in America, and if there's only one House of British Lords that meets in London, titled persons born in America are just going to move back to the Home Islands.
Well, the logical justification of the House of Lords way, way, way back was to have a governing house full of men who were landed (and therefor wealthy [and therefor educated]). That's what the original significance of titles was - not an extra thing to announce when you arrive at court but actual precidence over a patch of earth that could potentially make you wealthy. It's just that after half a millenium the link between land and wealth went and faded. Titles had a social value of their own, and so were worth getting even without land. Since most people who would receive them would already have land of their own, it was even in their interest to avoid grants on the opposite side of the country.
Still, IIRC, there remained on many estates privileges to the land in question. Exemption from property taxes was one of the latter day ones, although it's now disappeared completely. Since virtually any American granted a title of nobility would be landed, the natural thing in creating a new nobility would be to extend them the same sort of rights on their property, or even give them a further land grant.
Most new nobles would indeed quickly emigrate to London, but if they were landed, their families might stay behind. At the very least, they'll have a hired man running the place or collecting rent from tenants. Such people would have at least some degree of vested interest in America and be a true "American nobility." It occurs to me that the smart ones would stay in touch with events back home and function as mouthpieces for the first families in their province. The extent to which this happens would determine how the institution would last. On the one hand, these people are effectively the first representation of America in Parliament. On the other, few will be terribly enamored of men who become ennobled and immediately ship off to England.
As for American anti-noble feeling.... Well, keep in mind that by the mid-1700s the colonies were each run by a fairly small number of well-to-do families anyway.
They're certainly not going to be opposed to getting more official status.