The update: the batch of papers is still present, but smaller, and I have come to a batch that were not groan-worthy. Also I devoted two hours to research today, and that made me much happier overall, and better able to tackle the grading in a charitable spirit.
I have to admit that I was not so much pushing forward with the research as consolidating my current position. I owe something to my writing group this week, and so I took the 3600 words I now have in the draft of my article on manuscripts and cut it to 2500 by taking out most of the notes to myself, questions to be filled in later, and so on. I now have a tidy-looking document, complete with endnotes rather than bracketed chunks in the text, that contains four clear sections of argument, with two more to come. (Bracketed chunks are one of my compositional idiosyncracies: when notes disappear to footnotes or endnotes, I lose track of them, can't format them properly, and have trouble deciding whether they should be integrated into text or not. I need to keep them visible until I've moved them in and out of text a few times, and formatted references suitably for notes once I've decided they can go there.)
Although I know there's still a lot of work to be done here (a bit more on the fourth section; all of a long fifth and fairly long sixth section; then revision, in which I know from past experience a lot of the conclusion will migrate to the introduction, and then have to be replaced), I feel very encouraged by the experience of seeing 10 pages of professional-looking essay. The argument is somewhat dispersed, but it is there (I'll let the group mark the sentences in part 4 that need to get assembled in the paragraph that introduces that section; I can see they're not in the right places, but they exist, and right now I'm just happy that they exist). I'm on the right track. Progress has been slow, but I have made progress nonetheless, even while teaching 3 classes and serving on a time-consuming committee (of which more anon).
And I want to note, for my own future reference, that grading is easier after I write.