I would be more motivated if it felt like I was doing useful work

Are you sure? I wish this was what motivated me, but I've learned from writing about math for awhile that what I'm most motivated to write about is precisely what I'm most curious about at the moment. The usefulness of the writing has very little effect on my ability to actually finish it. (For example, I think it would be really useful to write an introduction to some of the material in Jaynes. But this hasn't motivated me to actually do so yet.) You should try writing a few things first, of varying usefulness and curiousness, and see which thing you actually feel motivated to finish.