It's important to keep in mind that the defining trait of an Ordo is that its members consider whatever they specialize in to be the greatest threat to the Imperium. Or at least the greatest threat that they feel they can do something about. Most of the Ordo Minoris didn't even have a sentence written about them. Just a single word or two in a table listing them. The Ordo Barbarus is one such example. Because of this, I'd say we're pretty free to theorize on their operations all we like.
I'd guess that there's some belief among these Inquisitors that pre-Industrial societies are more "pure" and their fall to heresy or corruption would be seen as an even greater tragedy. Kinda like how Asuryani can get ultra protective of Exodite worlds.
For the Ordo Astra, I'd say they're interested in being on the lookout for certain astrological patterns that can have ritualistic symbolism. "The stars are right" type of deals that are likely to bring out plenty of cults and degenerate groups ready to bring their master plans to fruition.
For your idea, the Ordo Redactus sounds like the perfect origin for him.
Ordo Minoris is just a catch-all term for any small group of inquisitors doing a specific job. Inquisitors can be independent if they want it's usually just easier to be part of an Ordo for resources and connections.
I would just note that there's a little more nuance to that. Ordos tend to be work that could apply to anywhere in the galaxy, or at least a fairly large area like the Eye of Terror.
Cabals are a group of Inquisitors focused on a specific example within their specialty. The Tyrantine Cabal was focused on the mystery of the Tyrant Star in the Calixis Sector. Or the Mycosapian Cabal, who are dedicated to rooting out an institution trying to create human-ork hybrids (I just made that up).
Conclaves are all of the Inquisitors that operate in a particular geographic area, regardless of specialty.