Ditching the whole host role would be a good first step.
That is one of the biggest things that makes The Twilight Zone what it is. If they get rid of the host, they might as well just use a whole new title.
The 80's version ditched the host in favor of a voice over. But they also showed Rod Serling in the opening so they probably did not want to try and fill his shoes.
The thing is that the 80's version was actually really well received and had a number of neat ideas.
On some level the revamped Outer Limits largely mined the same well as TZ. The original Outer Limits was more about creature features and weird Monsters/aliens where as TZ had the twist endings. Revamped OL borrowed alot of its ideas from TZ and took them to the next level. That the Outer Limits took the same route and ended up on TV for so long probably made it harder or the 3rd TZ to find its place.