It just seems like there's so much opportunity to play nice. Look at how LitVerse could play into the show:
1. Show's dialogue can just treat Data as dead without conflicting, because it's supposed to be a huge secret (for his protection) that he's alive, and other characters can still look at photos and miss him. It works on both levels.
2. Picard's done some shady shit and the writing on the wall in LitVerse is that he's about to have his (professional) ass handed to him. That can lead into him being situated wildly differently in 2399. It's a match made in licensing.
3. It's cheaper to use existing art designs (cough*new ds9*cough*titan*aventine*cough) than building from scratch, especially if you need "a ship for Riker to show up on" or "bajoran/cardassian episode setting." What I mean is that if they decide, for instance, that they want to show Titan, there is literally no good reason whatsoever not to use the Luna class design and call it Luna-class. To do literally anything otherwise, without compelling story reason, would be a deliberate middle finger to Lit fans. Say Picard needs a super-fast space ship that can only be used sometimes, for story reasons? You have it already. All you need is someone to complain "Too bad benamite crystals are so rare, or more ships could use quantum slipstream." That's one line. And you get Nicole deBoer to guest star; It's win-win. Casuals aren't going to fail to understand any of the above just because they haven't read the books. But you know what, it just might make them want to read those books... Hmmm...
4. If you want to use Janeway/O'Brien/Jake or whoever else, fine, just be a little bit hazy in show-continuity on what they might have been up to between 2379 and 2386. Then you have thirteen entire years worth of time in which to tenderize the characters into whatever the show's story requires. There is enough room in there for everything to play nice, if they only care enough. You can even have Seven of Nine, sans implants, and just not mention with great specificity exactly why or how they got removed. That's how they treated Geordi's visor in Star Trek: First Contact. All we saw was that his eyes were different now, and it was left up to interpretation. There's no reason they need to write a line that says "Doctor McCoy came out of retirement and removed my implants in 2381!" which would fuck LitVerse, when the same line can just be "I haven't had implants for some time now..." or even just nothing. "I understand you are a former Borg. / That is correct." LESS IS MORE.
5. Not for nothing, but the show could do whatever they wanted astro-politically... Hobus and Romulus could have galactic balance-of-power-altering ramifications, in other words, a convenient built in excuse from how things got from "Typhon Pact detente/maybe cold-war" to whatever space governments are supposed to be frenemies in the future Picard series. That's enough time even for something unlikely, like the Cardassians getting belligerent again, for example.
What is it Cameron Mitchell says in SG1's 200th episode? "Never underestimate your audience. They're generally sensitive, intelligent people who respond positively to quality entertainment." Or as Quincy Taggart says, "Never give up. Never surrender."