What I generally see with anxious perfectionistic gifted kids is that they tend to constrict the space within which they will allow themselves to work -- they will typically *avoid* the enrichment work or become really clingy/dependent while working on it.
That is EXACTLY what we see with DS6 and DS8. For example, this summer, DS8 took an online CTY critical reading course. He was happy to discuss the books with me, but when it came time to compose his answers to the discussion questions, it could take FOREVER! "Mom, may I have a snack? Mom, may I have a hug? May I sit on your lap? This is too hard. Will you sit with me while I do this?" Once he got on a roll, his answers would take about 15 minutes to write, but there were times when I thought he would never get it done.
The funniest part was that once he had written his answer, he was soooo happy with it, although he had to ask me a dozen times if I thought it was good enough. I saw small improvements over the duration of the course, but the work kept getting harder each week (not a bad thing) and DS frequently went back to the same behavior with many assignments.