Quote
"Teachers have a really terrible job. They have to tell students that they're doing things wrong all day long."

I would praise her for this insightful observation and the discuss the positive reinforcement techniques that the teacher uses. My daughter found it so interesting to learn about the negative reinforcement techniques that were used 'back in the day', and it helped her learn to appreciate her teachers.
Quote
On the other hand DD herself reflects daily on all of those occasions that she has been caught transgressing any classroom rules,

I would also praise her for reflecting back on her behavior each day.


Quote
"I don't know how my teacher could say that I had a good day... I had three markers and we're only supposed to have one. When she told me to put two of them away she was SO angry at me!"

This would be a good opportunity to make a a chart that shows the "levels of transgression". Make a list with her of all kinds of possible classroom transgressions, and then give each one a rank of 1 (minor) to 10 (really bad). Point out that a day with only a few 1's or 2's is a good day. She's falling into the trap that my daughter did at that age of strong emotions leading to 'black and white' thinking. By using cognitive strategies like this, we were able to slowly override the emotional black and white thinking.
Quote
At the end of the school day each day DD is absolutely shattered. She has NO resilience left. She often bursts into tears over the littlest thing, often on the way to the car. She spends most of the rest of the day being touchy, perfectionistic, and self-sabotaging.

The more tired she is, the more likely she's going to have these kind of emotional problems. Down-time and free time are so valuable and so underrated, in my opinion. If she's doing that well at play dates, I don't think she needs the social skills group, (but maybe they won't tell you that because they want your money). OT is not a proven therapy; it's possible running around and climbing on the playground is just as good. I couldn't afford OT for my DD - now at age 7, her sensory issues have mostly resolved themselves, and she's much more comfortable in the classroom environment. As for CBT, (which I assume is Cognitive-Behavioral Therapy), I wish I could have afforded this for my DD... but it all depends about the particular therapist. If it's a good one, your DD will probably enjoy going to him/her and will feel that it's helpful. If not, you may want to drop it, or find someone else. Since I couldn't afford CBT, I did what I could myself using books, such as "Freeing your child from negative thinking", and "What to do when you grumble too much". Great books. Highly recommended!

Downtime and freetime are the best medicine, but since they don't cost anything, no one is trying to sell them to you. I would strip down her schedule as much as possible and see what happens. The other thing I noticed was at that age, she needed to eat more often that she does now, and that fatigue along with hunger would really mess up her brain.

Good luck! Five was such a difficult age, but for me it has gotten so much better!