This is basically a heavy diplomatic focus with an aim to make integration into our alliance as relatively painless as possible for everyone. We wouldn't have as much centralized control, but would likely be able to expand further with this kind of approach than any other - military conquest as our primary means of spreading among reasonable polities is likely to be quite slow unless we either get lucky enough to have major support within a systems population (in which case diplomatic means of exerting pressure to change on the systems government are likely to succeed anyhow) or are willing to break out the atrocities (which I would rather avoid if possible).
It does mean that we might have to tolerate some degree of injustice continuing while we do our long-term political shaping, and that some of the architects of injustices might get away without a punishment, but I think that's generally worth it in the majority of cases if it means that we're forced to resort to military dominance less often. A lot of the atrocities which are common to less-developed worlds would be pretty easy to push aside through pure technological advancement changing the material conditions, too. Which isn't to say that military force should be entirely off the table, of course - there are lots of
unreasonable polities which we'll need major standing forces to deal with anyhow (Orks, Necrons, Dark Eldar), and if conditions somewhere are truly intolerable and negotiation is impossible, then the military can remain available as an option of last resort. I'd just like to avoid making it our go-to initial move.
Something like
ThirdComm from LANCER wouldn't be a bad thing to aim for, I think.
As for the religious aspect of it... I waffled a bit between State Secularism and Realmer Syncretism, but in the end Syncretism won out for me on pragmatic grounds - it provides a form of coherent culture that can help create ties across our new federation which might otherwise be lacking under a decentralized leadership style, the focus on syncretism should be relatively synergistic with the heavy diplomatic outreach, and it means that there will be an organization that's actually dedicated to looking at all of the various beliefs across our entire polity, and thus which can catch warning signs of corruption sooner. There's a risk of internal corruption within the organization, of course, but that's basically true of literally any major organization we build, and keeping the issue out of sight wouldn't actually solve the problem. At least this way we can have first-contact cultural specialists on religion who can sound an alert and who themselves can be regularly vetted.