I teach 8th grade math to special ed students and we started using sentence starters and hints or reminders on our tests for the constructed response questions. The students seem to respond much better when they have a little bit of prompting. Gradually throughout the year, we have scaled back on the hints so that they get used to self-starting, but it was a great way initially to build their confidence in that area. With appropriate accommodations, special ed students are very capable of completing these more rigorous assessments, but kids are also very perceptive of their teachers. If they can tell that you are overwhelmed by the increased demands, they are not going to have much confidence in their ability either.

I teach the same students, on the middle school level. Have you thought about using a writing strategy that will help them break down the question and outline their response? There is RACE or HOOT that are very effective. I don't think this new testing system is very fair for our students and I stressing for my students as well. Google HOOTS or RACE and see if that is useful.

First of all, and I know you already know this, but never let them see you sweat. I am in the same boat with my 9th graders and I have tried really hard to always use very positive and encouraging words when it comes to this topic. Perhaps only spend small snippets of time on this type of assignments. Create constructive response questions that are related to something in their lives and not solely the reading passage before them. When a shut down occurs, sneak in an activity that gets them up on their feet, engaged in a physical activity and then have them jump right back in. Also, see if you have have a yoga instructor come visit. They might have strategies to help your students relax, and relieve stress. They also can help set a tone for the classroom that encourages a more relaxed state and allows the students to face the writing with a breath of fresh perspective.

I'm assuming your Milestones are structured similar to mine, where the written portion only counts for a small percentage of the student's score. So that should reduce a bit of your stress. To help the students build stamina and motivation for the constructed responses, try daily practice where you increase their time/questions by 1 each day. You could make a chart to plot their growth and build them up for the big day. You could also build in rewards/incentives they achieve along the way to maintain engagement.

Break it down into smaller parts so they won't get overwhelmed

I teach 5th grade SPED this year. I would suggest taking it step by step by beginning with a sentence starter that may re-state what the question is asking. My students are used to writing one or two word answers. Another helpful tip if you are taking the test on a computer, start practicing now. I am luck to have a classroom set of laptops. We take those out and practice our responses. It made it fun for the kids and it keeps their interest.