Not Durin of course, but...well
1. Turoq is an ascended Daemon prince, he cast aside any real ties he had a long time ago. If he had anything or anyone he truly loved before ascending I'd imagine its gone, possibly sacrificed to fuel his ascension.
2. I think you are vastly over estimating our ability to even contact all these people never mind convince them to work together to create a fleet of any real effectiveness...
On the first point, yeah that could easily have happened, but people tend to form emotional connections over time. Failing to do so generally correlates with withdrawl from society, and would disadvantage a person trying to maintain control over a political organization and as such probably isn't something Turoq is doing.
On the second point, I still think it might be doable.
I'm going to elaborate on that.
It's about a year's travel out to Roskilde, which means that reaching anyone within 500 light years should be half a year or less to get there and a similar amount to get back. That's an entirely reasonable travel distance to maintain a close diplomatic connection and real life nations have done similar when facing travel distances of multiple years.
I also think that it'd be helped out by the way that Imperial Crusade Fleets were political messes of multiple groups that lacked the authority to command eachother showing up to help, each for their own reasons, and even inside of these organizations cultural and language differences could be debilitating.
There's institutional experience in settling those kinds of command issues and forging that mess into a cohesive whole.
But essentially what I think will be the best arguement in favor of it is the experiences all of the other Polities have suffered through.
Everyone else has spent the last thousand years gradually losing ground to enemies that are too mobile to respond to on the strategic level constantly puttering about and exploiting their every weak moment.
If you think we're frustrated with being unable to take the fight to Chaos, imagine how everyone else must feel.
Moreover all support for this scheme relies on a common root belief, namely that Chaos polities shouldn't be allowed to continue spreading and outcompeting uncorrupted polities.
I imagine every uncorrupted group agrees, but just isn't sure what to do about the problem.
An this really is only a small fraction of any one group's forces.
If that isn't enough we could try to convince the Blood Dragons, then rely on the fact that they've been interacting with these people for a thousand years and everyone knows the Blood Dragons are uncorrupted and(presumably) trustworthy. Maybe we could also lean on any contacts our surviving space marines made before entering the warp storm?
Finally, I'm not sure the roving Crusade fleet actually has to be that effective.
There are only a couple of scenarios I could see them being engaged:
What they would try do to screen a local campaign is essentially move the crusade fleet into the territory of whichever Chaos minor(10-90 worlds) they're attacking, then deny the enemy a chance for a decisive battle or a chance to trap them.
Under this scenario they would only fight to break out of a trap or exit a battle.
By doing this for a couple months they would be able to force the enemy to keep their forces screening their own systems until whichever local polity they are supporting can close the travel distance.
At which point they would take a secondary, supporting role in the campaign, still avoiding heavy casualties because we don't want to sour anyone we can sell on this idea.
Under this scenario they would only fight in a supporting role and avoid heavy combat.
They would also become engaged if the group they are threatening decides to give up and go for a mutual kill(or escape with their fleets intact) anyway, if that happened they would be assualting undermanned defences and taking ground fortificatiins with few or no soldiers in them.
Under this scenario they would be taking positions that are nowhere near as heavily manned as they were designed to be.
Keeping in mind that going for a mutual kill is still more practical for a Chaos leader than it is for us, as they would be able to transition their fleets into being a migratory warband more easily than we would. It's still an undesirable option for a Chaos leader to take, they lose their safety net and suffer a major defeat and embarrasment at the same time.
The final circumstance where the roving Crusade fleet might be engaged is if they were released to cover a polity against raids while they replace their forces after a mojor battle.
Under this scenario they might retreat if faced with a battle that might destroy the roving crusade fleet and would only engage against smaller raids.
None of these exactly require the best possible army, though I imagine many contributors will send their better troops, their long term survival could easily depend on the impression they make and the favors they earn with potential allies.
The major threats to this force would be traps and betrayal.
I imagine that every Chaos group that meets this in battle will try to trap them, with a trick, or a ritual to prevent them from escaping, keeping up with this will be a problem and will probably eat up a lot of Ridcully actions and local spy ring, Inquisition, and Adeptus Astra Telepathica resources.
The even more serious problem is betrayal, fear of it might actually be enough to prevent them from agreeing to the plan, they've suffered through betrayal as allies fall to corruption as often as they've suffered raids from faster enemies.
We could lean on any Space Marine reputation we could coopt, and I for one would be willing to put our money where our mouths are and trade away some tech in order to secure support for this fleet,
but keeping betrayal from killing this in practise would be a mild challenge and would once again be leaning on the Inquisition and Telepathica.
In summary I have thought a lot about how it might turn out and still think it's possible.
If we don't have the reputation or goodwill to draw on to make it possible we could try trading for a hero of the Imperium from another polity(maybe through the eldar?), by getting ahold of somone that everyone would respect to put in command of the hypothetical force we could push it through even if conventional diplomacy fails.