Use of "though" versus "however"
Solution 1:
You probably shouldn't use both but and though together like that, because you're saying the same thing twice; both words mark the clause as antithetical to what came before. So you should remove one or the other.
If you decide to use though, you need a comma before it.
I don't know whether it is new; it's just incorrect.
I don't think it is related to American English; I would simply interpret it as a typo, not as a conscious choice.
Both though and however are a bit informal at the end; though is better. The position of however in formal prose is rather at the beginning of a sentence, or after the first constituent.
Solution 2:
I thought it might be sensible to list the various acceptable alternatives:
E-books are on the rise, but they haven't yet totally eliminated the demand for paper books.
(Al)though E-books are on the rise, they haven't yet totally eliminated the demand for paper books.
E-books are on the rise, (al)though they haven't yet totally eliminated the demand for paper books.
E-books are on the rise; they haven't yet totally eliminated the demand for paper books, though.
E-books are on the rise; however, they haven't yet totally eliminated the demand for paper books.
E-books are on the rise; they haven't yet, however, totally eliminated the demand for paper books.
E-books are on the rise; they haven't yet totally eliminated the demand for paper books, however.
Solution 3:
The only reasonable answer to this question is that you must DELETE *though* because it doesn't belong there: it duplicates the function of but. However would be equally ungrammatical in the sentence:
E-books are on the rise, but they haven't suppressed paper books, however.
This sentence is grammatically incorrect.
It's not a new trend. EFL students have been doing it for eons. It's not just an American solecism. All native Anglophones have been infected by the Solecism iVirus ("i" for ignorance). It's endemic and epidemic wherever English speakers gather.
On a syntactic level:
Put a period before "though" and then erase "though".
Common = vulgar, crude, rude, inferior, low-grade, mean, poor, second-class, second-rate, shoddy.