I don't think the Orks would care who killed which Warboss. They're not exactly devoted followers. Killing an Ork leader will just force a mini civil war until a new one is "elected" then business as usual.
There are many reasons why a Crusade into the Koronus Expanse wouldn't happen. There happens to be one good one: because the dude's the GM and he wants to make it happen.
In a previous post I highlighted a few key things about the Koronus Expanse while bypassing a pretty major one: The Maw.
That thing is a strategic weakpoint. Yes, warp routes are always precarious things, but access to the Expanse is determined solely by this passage. A passage that is still wracked by warp storms and sudden gusts of aetheric winds to blow ships off course.
The very first step would be to secure this passage somehow. The Ordos don't shirk too much from heretical stuff, you can create a series of missions that will use devices to clear out and stabilize the passage or create new ones.
(In an abandoned DH campaign, I had come up with a device called the Pharos Mirror. It was designed by the Emperor Himself as a fallback for the Astronomicon, should humanity continue to depend on it. Its purpose is to reflect the Astronomicon and act like a smaller lighthouse. Lesser Pharos Mirrors would then reflect that "light" and so on, to make navigation somewhat simpler. The main Pharos itself had the ability to focus the Astronomicon's light to clean up an area of space from warp storms.
Recovering such a relic would stabilize the Maw or allow you to chart new ones.)
The second issue is men and materiel. The Imperium is at war, its factories are hard-pressed, its transports overburdened. This could all be handwaved away if the High Lords of Terra decide to invade and conquer the Koronus Expanse, of course.
But there's another way. What if the Crusade to take Koronus is really just a resource grab to fuel the Achilus Crusade. Going by threats alone, the burgeoning WAAAGH! from Undred-Undred Teef and the Rak'Gol pales in comparison to Tyranids, Tau, and Chaos.
So, instead of an official Crusade, your Ascended group can be sent to harness the Koronus Expanse. The side-effect would be turning it into a Sector as you secure new planets for their material resources as well as their "human resources" as tithes for the Munitorum.
The Expanse is mostly untapped, and with raw resources flooding into Calixis, or better yet, local Koronus factories, they can churn out materiel. A portion would be retained for defense and for a lower-grade Crusade.
Instead of fleets of hundreds of ships of the line, think scattered, patchwork alliances of Rogue Trader fleets who are constantly weighing the benefit of every action. Keeping them together and on point while balancing their influence and keeping them competitive will be a handful. A Rogue Trader civil war (of at least three sides) is certainly possible: Loyalists, Independents, and Opportunists.
I think that's more suited to the Koronus Expanse due to its geography and history.