Grayven is having a more positive Impact that the more "Not really Heroic" version, and he is a New God of Conquest.
To use a metaphor that I recently read in Obloquy's Life Ore Death, I think that Grayven is better at weeding (decreasing the bad by eliminating deleterious entities and groups, most notably the original Light) while Paul is better at planting new flowers (increasing the good via fostering collaboration and innovation, building infrastructure and empowering people on a wider scale), which isn't to say they never overlap.
One thing that's increasingly an issue for me is the lack of onscreen discussion and planning on actually eliminating the Light, which would be the rational, non-traditional course of action, essentially going back to the 'villains act, heroes react' trope that Truggs is so fond of. It was great seeing Paul and co. deal with Satanus, but there was build-up for that in several previous episodes, starting with creating an angelic Blaze, while there doesn't seem to be much planning to deal with the Brain or Savage, who are the most overt supervillains of the group. Honestly what I want to see (though I'm aware the story isn't obligated to go exactly the way I want, and would likely be boring if it did) is Paul actually using all that wealth of his, plus his connections to Kordtech, Oliver Queen and Wayne Enterprises (or whatever its name is) to stage a perfectly mundane corporate takeover or at least undermining of Lexcorp; I thought the Kraft-Cadbury storyline, while amusing and good at fleshing out the world, was foreshadowing for Paul doing the same with the corporate and industrial base of a man whom he may like and admire, but consorts with demon lords and madmen in hypocritical and just destructive ways.
There's none or at least far less of the proactiveness that characterized early Paul, and while he admittedly has galactic concerns as well, Earth is special, both to him personally (which is significant for an Orange Lantern) and just metaphysically, considering the Life Entity and general metaphysical power focused on the planet. I'd be happy if we saw that other characters were discussing or doing something about it, but this is still a story that's largely from Paul's perspective and I think it's very in-character for him to want to deal with the Light in an effective manner, which to my mind means striking before they have time to plan and build, which are their main strengths. I'm not sure how much of Season 2 events are still going to be present in this fic, though I believe there are some general ones, but I can't really picture that happening in any believable manner, given we have four in-universe years before that, and frankly if the Light is still around then that's just incompetence.