Just done my FI(A) in a Slingsby. Like you I was very worried about the spinning.
After the first one I was fine. It's the fear of the unknown, coupled with those deep ingrained words from previous instructors, which quite rightly put the fear of God into you!!!!
You'll be fine. I found it the most useful and interesting part of the course.
In the right aircraft, it can be quite enjoyable!!
LJ