Hey good topic!
Why assume that TNG should go forward as planned? I'd jump right over TNG and start with DS9 (assuming that people like Alexander Siddig would still be old enough for their roles). Maybe I'd keep Data and the Borg (but no Queen and no credibility-destroying overuse). Possibly I'd keep Q because of DeLancie, as well as Worf, Gowran, K'eylar, and the Vulcan-Romulan unification concept but wow thinking it through, we could really lose almost all of TNG without much bother. That's a pretty scant list for seven seasons and several movies.
I'd either go right to DS9 or use the DS9 approach for a ship-based show - serialized, take consequences seriously, don't shy away from conflict within the main cast, do whatever it takes to avoid being vanilla and bland - but stop well short of the BSG level of darkness because that's outside the boundaries of Trek.
I'd keep as much or more from VOY as from TNG - the whole cast minus Barbie of Borg and Neelix, and the basic concept was fine. VOY really needed the DS9 approach. Really dig into the idea that they are lost on the far side of the galaxy, without Federation resources. Keep the notion that not all the cast even wants to return home. They're explorers - wouldn't their "predicament" be seen as a gift to the really intrepid people among them? Not everyone is going to have loved ones waiting for them back home, or at least loved ones that they wouldn't give up for the opportunity to really fulfill their destinies as explorers.
Use the DS9 approach and many premises could work, even the much derided or hashed-over ones like Federation Civil War, Fall of the Federation, Starfleet Academy, Navy SEALs (the Maco concept), Section 31-based series or Alien-Centric series.
More than the content, what ails Trek on TV is business oriented. Trek is pricey to produce and because it's a premium brand, the owners wouldn't want to relegate it to low-rent Skiffy or other basic cable. It really is best suited for a network, but networks aren't best suited for Trek - they are trending towards the lowest common denomenator while all the interesting and genre based stuff is migrating to basic and premium cable. Maybe an HBO-junior basic cable network like AMC or TNT would be "premium" enough for Trek.
It's called "Star Trek" So being "about the bridge crew on a starship who encounter alien worlds and the various kinds of crises that can occur aboard a starship." Makes perfect sense. It's all about how you execute it.
Trek actually means a journey to a destination - a migration to a certain place with the intent of settling there, and without necessarily being interested in anything along the way. The one thing Star Trek has never been about is "trekking."
I think that DS9 was the series that got stale ...
It is certainly the series that viewers began to abandon, almost immediately.
The initial version of "Yesterday's Enterprise" was pitched by Eric Stillwell and his writing partner; Eric had been an employee of TNG for years at that point.
That's a chart of TV business trends during that time period. Network TV suffered a hemmorhage of viewers to cable (which continues today). It has a lot less to do with the actual content of the shows than everyone seems to assume, and would have happened regardless of the content, topic or approach.
The more relevant concern is, given that network TV is now inhospitable to anything but more-of-the-same doctor/lawyer/cop shows, sitcoms and reality TV - and the place for the likes of Trek, or anything creative or nichey, is now low-rated basic cable, which would have a hard time paying for a pricey sci fi show - how can the business model be devised that will allow Trek to return to TV?
And forget HBO and Showtime. Trek is too unmainstream for network TV but too mainstream for pay cable. Unfair, I know...
The only way content factors into the business situation is that the bland homoginized TNG approach would be the worst approach. The mass market won't watch Trek on TV. To survive, wherever it lands, Trek needs to take some degree of nichey approach.