If you aren't ready to take the no-grade plunge (or your particular corner of the pool will never support that choice), there are still ways to shift your thinking about assessing student writing.
One of the biggest is to move away from focusing on deficits and mistakes.
Avoiding mistakes is not a useful focus for writing. For one thing, not making mistakes is an easy path to mediocrity. You can play the game without making any mistakes and still lose. You can perform the piece of music without a single wrong note or missed entrance and still be boring and bland. You can step out on stage, remember every line, hit every mark, and still be forgotten five seconds after the final curtain falls.
It is not enough to not do something wrong. You have to do something right. We've reached the point where software can write mediocre essays, and we've been stuck for years at the point where software can tell if a student has produced, at best, a mediocre piece of writing (though it also may fail to notice if the essay is far worse than mediocre). That's because all software can do is sample a gazillion chunks of what has been written before and kind of mush together and spit out a homogenized version of it.
Human writers should do better than that. They should bring something new to the table, some piece of their own personality, some synthesis or growth that's new to them. They should strive to be more than safely bland.
For the classroom teacher, fostering the braver, better attitude means a particular mindset. It is easy, especially if you are not super-confident about your writing instruction and assessment skills, to stick with the deficits and mistakes model, to spot the student 100% to start with, and the subtract every time you find a problem. It's easy for everyone, and students recognize the model from every test they've ever taken where the teacher's role is to "correct" the test by marking everything that's "wrong."
But the lesson here is to take no chances, attempt nothing you're not certain is okay, The lesson here is to be the person at the party who says nothing that might bother anyone, so that at the end of the evening you have offended nobody--and nobody remembers who you were. The lesson is to be a timid, mediocre writer who gets by.
Work with a positive focus. Spot your students 50% for getting words on the paper, and then start awarding points for what they do right. Give them back papers that include circles and underlines and exclamation points next to the best parts. This gets them to stop looking for red-lined "mistakes" to avoid next time and moves them to focus on what they could strengthen, what strengths they have to build on.
Doing so not only makes for better writers, but it more clearly turns writing assessment into writing instruction. Focusing on deficits and mistakes turns assessment into whack-a-mole, only your students are the moles and what they learn is to never stick their heads out of the hole. Focusing on strengths and growths is about feeding the plants in the garden and helping them grow.
There are other ways to implement this sort of change. I love the teacher who has her students aspire to get a "publishable" at the end of rewrites. Or "3" if it's a rough draft, "4" for the edited version, and "5" for a final copy.
I'd also argue that this mindset is useful in classes outside of the English department, and that using this approach is what elevates written assessments above simple objective tests, no matter what the content is.
As with all advice about writing instruction, there is nothing new here, nothing that lots of other writing teachers don't already know. Still doesn't hurt to repeat it. Also, hat tip to John Warner whose piece took my mind back to this aspect of writing instruction.