MarkB
Legend
The Novels that follow the TV Timeline (Destiny and Typhon Pact Series) include a final showdown with.... Setting the TV Show after these events makes sense. The crews of the Enterprise and DS9 are all split up. Riker and Geordi are captaining their own ships. Worf is back on the Enterprise with Picard and Beverly, Data is still "dead". Janeway (to most of your delights) is also dead and Voyager with most of its previous crew has returned to the Delta Quadrant with a fleet of 9 other ships via Slipstream to continue exploration, look for the Borg and establish diplomatic relations between whomever is out there.The Borg. It is a major apocalyptic event. Thousands of Cubes invade Federation Space and destroy a massive fleet assembled that includes Federation, Cardassian, Klingon, Romulan, Gorn, Breen and even Ferengi Ships in seconds. Many worlds are completely and utterly destroyed and made lifeless, starbases vaporized. It spurs the creation of the Typhon Pact, a sort of Anti-Federation which includes the Romulan Star Empire (but not the Imperial Romulan State), The Breen, The Tholians and some other minor races. The Borg however are finally and truly gone, though the Federation doesn't believe it. The fallout is intense, Andoria leaves the Federation...
It's a perfect setting for a new crew to tell it's own stories with regular checkins and contact from the previous older crews. The Federation has no choice but to use younger and slightly untested crews as they struggle to explore and rebuild and deal with the new diplomatic landscape. It's just the perfect setting for a TV Show and changes some of the previous crutches (no more borg yay!)
Whilst that does sound like it has potential, I doubt the new series will use any continuity beyond the TV series and movies. Although the novel lines have, in recent times, tended to do well in terms of cross-consistency, the franchise as a whole has never really tried to maintain a consistent "expanded universe" in the way that, say, Star Wars has - and even Star Wars doesn't bother to pay much attention to EU continuity when it comes to movie or TV plotlines.