I think you're going to run into a few problems here.
Even if you get agreement from a few people here, there's just no way to enforce consistency or get anyone to buy into these definitions. People can't even agree about the name of that movie that came out in 1977 ("It's A New Hope!" "No, it's Star Wars"), let alone more arcane technical definitions. Every definition here potentially overlaps multiple terms.
Even assuming we allow for great flexibility, these terms are hierarchical. Some are subsets of others. Some are distinct. Some are partially overlapping and partially distinct.
Anyway, here are my personal definitions not based on anything authoritative other than lurking around here for a while and seeing the sort of things that go on here:
Fan Preservation can be used to describe ANY attempt to preserve a particular version of a film for posterity. It can include unaltered preservations of a single rare release, it can be a remux of different releases, it can be a reconstruction of an original version from multiple sources... it could even be a reconstruction of a particular modified-for-television broadcast version of a film. It could just be transferring an old VHS bootleg to DVD.
Fan Restoration is a subset of the above. It's an attempt to restore a particular version of the film that is otherwise unavailable, in a way that involves a lot of processing to bring out qualities that weren't present in the unaltered source material. Project Blu would qualify as a single-source fan restoration, the Despecialized Editions would be multi-source.
Fan Reconstruction is a subset of the above, and it's the multi-source version.
Fan Extended Edition is a subset of Fan Edits, where the primary goal of the project is to add material to the film.
Fan Remux is a subset of Fan Edits that overlaps Fan Preservation (if the goal of the remux is to preserve a particular version), but can also include making unique new versions.
Fan Edit overlaps Fan Preservations and Fan Restorations, and is a superset of Fan Reconstructions, Fan Extended Editions, and Fan Remuxes. Basically it only means the fan did some editing to the sources. It does not imply what the purpose of that editing was. It could have been to make a home video release like the theatrical version, it could be made to shorten or lengthen the film, it may have been only audio editing, but it wasn't a simple VHS-to-DVD transfer, for example.
Workprints and Bootlegs should be separated out. Workprints are film elements from the official process that produced the film that didn't make it into the film itself, while bootlegs are unofficial audio or video recordings of a particular "performance" of the film. In-theatre tape recordings, VHS tapes of TV broadcasts, etc.