If I'm being perfectly honest, I was one of those people who didn't even know about Green Lantern until I watched Justice League so I don't really think its hurting him. Whats hurting is lack of attention on him (of course I stopped reading GLC 3 issues in so that could have changed).
Pull List: (Marvel) Daredevil, Gambit, Hawkeye, Ultimate Comics Spider-Man, Uncanny X-Men/Avengers, Waid's Hulk, Young Avengers, Fearless Defenders (DC) Nightwing, Batman, Wonder Woman, Animal Man, JL
What should've been done in the Nu52 is give John Stewart his own series. I would still have him as a Green Lantern but the ring would be more secondary and the series would delve more into John's character and his history according to the New 52.
In my ideal John Stewart series, he would be a special agent in the GLC. His position would allow him to go on undercover missions or Black Ops type adventures. There would be a lot of intrigue and suspense in the new series and I picture it reading like a spy/mystery novel. In fact the title of John's new series would be MYSTERY IN SPACE. The underlying theme here would be either to uncover the mysteries of the universe or to protect it from those who might exploit it for their own ends. In the series he'll be part of the Navy SEAL equivalent to intergalactic peacekeepers called KNIGHTS OF THE GALAXY. John will also undertake missions that challenge or test his morals or values (ie dealing with a corrupt planetary regime that made backdoor deals with Oa or the rising fanaticism of The Manhunter Cults or hidden cells of Weaponers of Qward.). We'll also see flashbacks of John's time in the military and why he decided to become an Architect when he got out.
That's how I would do it!