JACKPOT, I had a thought about this after posting it, and after a bit of tweaking, I managed to get it to work as a job.
Seeing the hospital job kick during Shatteredlines made me realize what was missing. The rest job (which has flags->special set), HAS to land in the hospital. As soon as I did that with a specifically marked hospital zone. My Animal Caretaker/Doctor took off and did his job.
I also realized you can mark a hospital as a pen/pasture, and I realize while I may not be able to get recover wounded to work, I *can* generate pen/pasture jobs on the fly in their place, and simply get them to drop an animal on exactly the right space to get the hospital to work.
EDIT: I need to experiment more with Recover Wounded, although part of me feels like Pen/Pasture may be more approiate.
EDIT 2: As long as the job doesn't land in a bed, everything works perfectly. Though I've yet to manage to injury an animal in a way that requires traction (its possible only something humanoid can be tractioned)
EDIT 3:
I'm fairly sure its possible we might see a cat crutch walker if there isn't logic to prevent it It appears there is active logic to prevent pets (or non humanoids) from getting traction or crutches; forcibly setting those flags are cleared immediately in the next tick.
EDIT 4: I'm open to ideas how this should work; since I can make the job basically land wherever I want, I'm wondering if the correct way to handle this is to have an animal chained up, which would mark the spot where they should land; like a bed does for a dwarf, then you can put a table and a traction bench next to it. Though IMHO, surgery seems to go find on animals w/o one ...
EDIT 5:
I'm vaguely curious if a chain in hospital in a hospital zone might just make it work ... the dwarf that got healthcare in Shatteredlines did not take the rest job as far as I could tell. MORE SCIENCE! Nope, causes the rest job to cancel; I have no idea why it worked in Shatteredlines; maybe the rest job was actually there and just hidden.
EDIT 6: Since you can use this job to basically get an animal to go anywhere on command, there are interesting possibilities; you could easy cook up a mode to actively have a squad of animals to go X/Y/Z.
PTW. If you manage a binary patch to let wounded aminols be recovered, may I include it in the Modest Mod?
I'm going to post this as a merge into DFHack proper, under an open source license. You're welcome to include it in Modest Mod (or whatever), though I'd appreicate it if you credited me.
EDIT 7: holy ****, I just realized the full implications of what I could do with this; I can generate jobs related to animals on the fly, *including* give food/give water; finally a way to get animals in *general* fed and not depend on owners.