I'm so sorry you are having to go thru this because I know it's so stressful for everyone involved. These are all great suggestions, and I think we are all on the same page. I can tell you that when I was a child I was SUCH a mama's girl and when I was away from my mom I was worried about HER because she said she missed me. I felt like she was sad. Clearly as adults when someone says we've been missed we take it as a compliment but a 3 year old takes it at its most basic meaning, that we are sad when we are away from them, which of course makes them sad, too. Your new approach should definitely help a little bit, but obviously hasn't solved the problem completely.
As for the rest of it, I can tell you we experienced something similar last year when my younger child started 1st grade. He had also been in daycare or school since around 10-12 weeks of age and had never had any reservations about school which made it more baffling. When school started he cried almost all day, EVERY day, and we were all stumped. He said he liked his classmates, his teacher, he denied being bullied. I'll spare you every attempt we made to solve it but will tell you what FINALLY helped: a written schedule. I was so skeptical when they suggested it, but his teacher made him a photo schedule of his day, like putting coats/backpacks away, first lesson, snack time, recess, lunch, etc. A little photo of every activity and a box to check each item off as he finished it. Then he could see how close he was getting to the end of the day and going home and it WORKED! I really couldn't believe it but it might be worth a try for you! Best of luck!