Digital preservationistas rejoice?
I managed to get FITS integration working in Islandora via a plugin. The plugin will automatically create a FITS xml datastream for an object upon ingest in the Islandora interface for a given solution pack. Right now I have it working with the Basic Image Solution Pack, Large Image Solution Pack, and PDF Solution Pack. You just have to make sure is in your apache user's path (thanks @adr). [UPDATE: Works with the Audio Solution Pack now.]
What I had feared was going to be a pretty insane process turned out to be fairly simple and straightforward, which I'll outline here.

  1. I looked at existing plugins for something similar that I could crib from, and found that something in the exiftool plugin which is used in the audio and video solution packs.
  2. Using the existing plugin, I ran some grep queries to figure out how it is used in the overall codebase (Islandora, and solution packs). 
  3. Created a feature branch
  4. Hammered away until I had something working. (Thanks @mmccollow)
  5. Create an ingest rule for a solution pack. This tells the solution pack to call the plugin.
  6. Test, test, and test.
  7. Merged feature branch with 6.x branch, pushed, and opened up a  pull request.

That is basically it. Let me know if you have any questions. Or, if you know of a way to make it even better, patches welcome ;)
[Update #2]
I've added a configuration option to the Islandora admin page to enable FITS datastream creation, and the ability to define a path to I put it in the advanced section of the admin page which is not expanded by default. This will probably be problematic, and folks won't notice it. It might be a better idea to collect all the various command line tools Islandora uses, and give them all a section in the admin page to define their paths.
I also have FITS creation working with the Video Solution Pack now. Up next, Islandora Scholar... just have to get that up and running ;)