Regarding April's command in the comic, I do wonder if that might be the Abrams-verse version of the Constitution-class
. And as others suggested, with a less legendary registry. Technically to be in the Enterprise lineage it need only carry the name and 01 within its registry. Again, slightly more advanced since the Narada incursion of 2233. Yet scaled within comfort levels of some of us die-hards.
If so, this could make the oversize Starship-class
actually plausible as read on that dedication plaque on Pike/Kirk's bridge. It would certainly put that old chestnut to bed in this case.