Any new series may have Trek's background as a hindrance. I would gloss over Trek's continuity if it's in the old timeline and set the show in the 25th century. Familiarity but new, that is key...
It worked for the TNG in the 24th-Century.
The real key with any
continuity--regardless of its size--is not to get bogged down in the specific details, to use only a little bit of it briefly in passing in throwaway lines a small handful of times like TNG did. That's enough to give any fictional universe a sense that it wasn't just created overnight, IMO.