I have had a lot of luck in the past by observing the teachers of the next grade in the spring to figure out who would be the best fit. I then write the letter to describe what my child needs tailored to that person within the confines of the rules.
Flexibility is a good substitute for term differentiation
Compassionate is a good substitute word for "nice"
Classroom management is a good substitute for discipline
It also works well to have a verbal conversation with the present teacher about your child's needs. That person will have seen it first hand, even if it's not interpreted in the way the parent sees it. In our schools at least, they are key participants in the placement decisions.
That's essentially what I did when dd13 was going into 2nd and we were told the same thing: no specific teacher requests, but we could describe the learning environment our child would do best in.
Dd's 1st grade experience was so bad that I homeschooled her for the end of the year in 1st. I didn't want a repeat of that so I probably carried it a bit further than geofizz. I went in and spoke with all of the 2nd grade teachers and essentially interviewed them. I knew which one we wanted so I described her down to stating that dd felt more comfortable with blonds b/c they reminded her of mom -- lol! I had been such a pain in their rear the year prior that they gave me what I wanted although I know that it was highly transparent.
