Based on how he reacted to the TOS Movies, anyone who thinks Gene would've approved of DS9 is out of their mind.
And based on what I read about his kept-out-of-public misogyny in the second volume of
The Fifty-Year Mission (which covered from TNG on), he wouldn't have approved of VOY because he wouldn't have been able to get behind a woman Captain as the series lead. So that would likely extend to DSC as well. Burnham's not the Captain (at least not yet), but she's still the series lead.
PIC is pretty similar to the TOS Movies or, when it's not, it's taking a different track than the TOS Movies did to show how Older Picard is different from Older Kirk. But, like with DS9, if he didn't approve of the TOS Movies, he probably wouldn't have approved of PIC.
Oh, and Gene Roddenberry wouldn't like what they did with the Vulcans in ENT, so that's out too.
Really, all you've got left that he would've approved of would've been the Abrams Films... oh, wait a minute,
nooo, Vulcan was destroyed.
Okay, so we're shit out of luck.
PS: We can't go by anything Rick Berman said. That's just PR. What was he supposed to say? In one sense, he probably just thought "If it ain't broke, don't fix it", and he'd say whatever he had to in order to keep the Roddenberry Faithful loyal.
Which is probably why Ira Steven Behr drove him up the wall. Can't spin the Holy Gospel to The Chorus when Ira's got the Dominion War going on and he won't back down.
But now, here we are 25 years later, having to hear The Chorus. The difference is: Rick Berman put more effort into spinning and telling people want they wanted to hear. Alex Kurtzman doesn't.