According to the timeless perspective, the person-moment who "began reading the sentence" and the person-moment who "finished reading the sentence" are fundamentally different entities, coexisting eternally in a universe where nothing actually changes.
The only problem here seems to be the incorrect application of English words and intuitions to more complicated physical propositions.
The main problem is that in a timeless universe, there is no time, therefore there is no change, therefore no thing can become another thing, therefore the person at the beginning of the sentence can't become the person at the end of the sentence.
Maybe you have a timeless definition of person as a set of person-moments, and this allows you to nominally regard the person who started reading the sentence and the person who finished reading the sentence as parts of the same overall person.
Nonetheless, the denial that time exists implies a denial that change...
If it's worth saying, but not worth its own post, even in Discussion, it goes here.