Effective Strategies Exist for Managing the Paper Load
You don't need to grade the writing, just the subject-matter. While it's not possible to truly separate writing from content, your expertise is in the latter so it's not necessary to worry about grading the former. Of course, if the writing is so poor that it gets in the way of making the content understood, it's certainly appropriate to "take-off" for that.
Every paper need not be graded or even given credit. This may be a controversial statement, but all papers don't need to be graded. The purpose of the paper is to get students to think. You don't need to assess that thinking as writing. Suppose, for example, you give students a writing prompt in class based on a reading assignment. After a few minutes of writing, you hold a discussion on the topic. You can assess students' oral contributions. They need not even turn in their papers.
Shorter papers are often better than longer ones. How often in our professional practice are we asked to write papers of a minimumlength? It is far more likely that we will have a length limit. Asking students to condense their thinking is good practice on several levels. For one thing, it makes them think carefully about what is important and worthy of retaining, rather than the more common practice of padding the length. I tell students to think in depth, but then explain as concisely as possible.
Large papers can be broken into parts which are reviewed/graded consecutively over the term. This spreads out the burden of grading, and gives feedback to the students before the end of the project. Students are more likely to pay attention to those than comments to be picked up with the paper at the end of the course. In addition, one need not carefully read the earlier parts on the final draft.
Rubrics make grading more efficient Basic rubrics for minor papers can be as simple as awarding a 'Plus' for a paper which shows genuine engagement; 'Check' for a paper which goes through the motions; 'Minus' for a paper which misses (or +2, +1, 0) on a rubric for specific points.
Consult with your writing center (or composition faculty) for more ideas. If your institution has a writing center, encourage all writers to use it, not just those with severe writing problems. Explain that writing center conferences can be particularly valuable at the start of the writing process before the writer has even produced a rough draft. Writing centers can also help instructors design better writing assignments.