There doesn't seem to be any intractable friction from their presence here, although she's sure they'd like to get back to being their own society eventually. Their settlement was torched after everybody was out so there is currently nothing for them to go to. The fact that she can't sense Maiar, however effective she is at killing them once she knows where they're at, is a major drawback to her trying to defend anything being concertedly attacked with no Maiar assistance; she supposes she could try to hire Thuringwethil for a longer-term engagement or something and try to get another Dwarf- and rock-music-assembled city set up for them over a few years (if the Dwarves will extend her credit or declare that her IOU for the science lecture and couriering is valuable, or give her more couriering jobs she can now complete in moments).
Another advantage to a larger cargo limit is that she can become very very wealthy very very fast by doing shipping among the seven Dwarven kingdoms, come to think of it. The Men are welcome here for as long as it's needed and may use the rock-music-songs to build a new city when seems fitting. They are unenthused about hiring Thuringwethil but suppose that's an option.
Well, if anybody wants to suggest a Maia who is more of a free agent than Huan or Melian and more with-it than the river Maia she's open to suggestions but it seems like very few Maiar show up to work on this continent.
She expects very little from Maiar, but unless anybody knows how to etch those repelling sigils into goggles or something so she can see them...
Then the Men are probably staying put for the foreseeable future unless she works something out with Thuringwethil and develops enough Dwarf-related purchasing power.
Loki goes back and makes it known to the Men that they are probably staying here for another few years at least; she needed help to kill Sauron and help lives here and may be hard to come by elsewhere; but she is going to look into ways for them to go be on their own, it just might take a while. They should definitely let her know if they need anything to be comfy here for the next several years.
She is sure they can find useful things to do. She hears somebody's going to try to learn to do magic music, is that right? And there's other work around; she is sure they can learn anything they'd like to try if they're feeling at loose ends.
If they would like to find out what there is to do in a less haphazard way than wandering around and communicating telepathically with Elves who may not have picked up their language yet she can ask!
So she asks. Maitimo? Have you got anything useful for Men to do?
Honestly, no. Once enough people have learned their language I could put them on the regular work rotations but my current vague sense of the capabilities of Men is that they wouldn't be able to keep up? And giving them half-shifts with breaks and arranging for their pace not to matter is more work than letting them be. I can invent things for Men to do if Men require things to do.
On the higher conscientiousness end - and those are the ones who are not just enjoying the idleness in the first place - they can put in about as much consecutive work as I can, complete with a similar tolerance for sleep skipping and missed meals. You could put them in separate groups if it would be awkward to have them working to different schedules, but I assure you being unable to go without sleep for a week does not inherently make a person useless, they just have to learn to do other things. They can cook; they can learn your recipes. They can farm; they can learn these crops. They can scratch Maia-repelling sigils into stones; they can do it in their apartments if it would irritate people to watch them putting down the tools for a moment to get lunch.