Do any of them happen to be departing in a direction that is not worse than orthogonal to their ideal return route?

Currently none of them are departing in any direction! In theory that could change if they waited long enough, but it's also possible they would just stand around for several more hours.

"Unless you know how to provoke one of them to do that, it's a long time to wait."

"I suppose that is probably true. ...If we are able to find one example of a relevant object, it will likely be easier to locate others, either through Locate Object in likely locations or through Discern Location."

None of them are anywhere near eighth circle. ...well, not yet, anyway.

"Well," says Blai, "if you come to a conclusion about what we should be on the lookout for, of course you may let us all know."

And they can start hiking back to the troops.

They are briefly harassed by a vrock telekinetically hurling a large rock around, but it teleports away when it realizes that their group has a large number of unarmored people because it has a lot of casters rather than because they're incredibly broke.

...His guards are concerned about the fact that his group appears to be missing one of the humans he departed with, while containing an extra fox-like individual who was not present when they left and who claims to be the same person. They would like to do some extra security checks, please. 

Completely reasonable, here is his account of what happened including that she's acting in-character for Nenio but check away.

Then they will go through various magical and mundane checks! ...Somewhat more of them given Nenio's memory issues and inability to recall various past conversations! But eventually they are satisfied that Nenio is in fact herself and that no one involved is likely to be enchanted (though they do remark to Blai that the lingering aura of the spell that affected her is still present.)

"It startled both of the other wizards when they looked at it but that's still remarkable staying power," Blai agrees.

Maybe they should keep an eye on her overnight just in case it turns out to be complicated somehow?

"I am willing to acquiesce to that on the condition that I am permitted to interview you for my encyclopedia."

"You will have to spend some of the night asleep," Blai points out to Nenio.

"I am willing to refrain from questioning them while I am asleep."

In that case observing her overnight seems harmless unless the prospective interviewee is for some reason wildly uncomfortable with the concept.

It's not the most ridiculous request they've ever had to accommodate from an adventurer-wizard, they can cope.

His staff have status updates for him! These include: The army was menaced by a small group of vrocks, but the paladin-archers successfully drove them off! His scouts think there's a larger group of demons planning to engage his army within the next couple days; it seemed like they were Dominated, which will probably make the battle a bit more protracted, since they'll presumably be under orders not to flee. Here's what they know about the current size and composition of that force, but more demons might teleport in. They have procured and hung strips of fabric in the command tent as requested! (This involved more people than usual being in his tent, but they have checked and verified that there are almost certainly no more people involved.) Also, the Abadaran has an update for him, though of course it would be perfectly understandable if he were too busy to have the chance to speak with him.

....why would he be too busy to speak to the Abadaran he only recently hired specifically to give him updates on Abadaran things while he's visibly just standing around hearing reports at this moment.

Well, managing the Crusade is surely a lot of work, no one here would think it reflected badly on him if he wanted to prioritize more urgent tasks.

The Abadaran is wondering what specific commitments he's made surrounding behavior from before he took over the Crusade, and, in light of any such commitments, what he would like the Abadaran to report about people for whom he discovered financial malfeasance prior to that point but who have refrained from malfeasance since.

Blai has not made a lot of explicit promises about that but considering the circumstances would prefer not to go after anyone who has both of competence with figures and sufficient self-control to manage under a Do Not Steal Things regime, even if they behaved differently before. That does not mean he's obliged not to find out who they were but makes it pretty low priority.

Understood.

He investigated the following people today! The person accused of embezzling by their rival was in fact embezzling. He determined upon further investigation that his commanding officer was aware of this and encouraged it to continue in exchange for receiving a cut. 

On the bright side, he did identify the following person who has not engaged in financial malfeasance since the Knight-Commander took over (although the obvious inference from the remainder of the conversation is in fact correct), and the following additional person who was extremely strict about assigning pay deductions for anything that could even arguably merit one while intending to pocket the money but handed over the money for the army's use once the Knight-Commander clarified that he was not allowed to keep it.

Right. Blai appreciates the Fiducia's diligence and will go congratulate the ones who shaped up and deal with the ones who did not do that.

The guy who was accused by his rival is going to (seemingly at random, he doesn't appear to be aware of who reported him) accuse him right back. It's not fair to go after him and let people like that run loose.

Does he have any evidence? Would he like to volunteer to cover the costs of the investigation should it prove fruitless?

His evidence is that he's sure the man was doing it before the Knight-Commander took over and he doesn't seem like the type to have stopped. He'd be happy to cover the costs if it weren't for the fact that he's being removed from his comparatively-well-paying post.

He is, yes, and for reasons that call his credibility into question. If the guy is in fact pulling anything like that he will be caught eventually, by the audit or a Zone.