stats; dependent proportions; not binary; 4 'groups'

I have some dependent, nested proportions that I need to compare and I have no idea how to do it. Here's a fictional, analogous example.

I gave 6 people a test and recorded their behavior with a video camera as they took it. Each person got some of the questions wrong (wrong answer = WA) and some of the questions right (right answer = RA). While the people were answering each of these questions, they were also engaging in other behaviors, including pencil chewing (PC), leg tapping (LT), looking up (LU), and looking down (LD). I realize that these aren't actually mutually exclusive, but please just pretend they are for the sake of the example.

Once I had all the data, I figured out which questions the participants got right and which questions the participants got wrong. Then I assessed what percentage of time spent answering each question was devoted to engaging in the above four behaviors.

Here is some example means, coded as indicated in the text above:
WA-PC: 40%
WA-LT: 30%
WA-LU: 20%
WA-LD: 10%

RA-PC: 35%
RA-LT: 40%
RA-LU: 10%
RA-LD: 15%

Here is an interpretation of one of these values to clarify what's meant...
"WA-PC=40%" means that, "while the participant was answering questions that were subsequently marked as 'wrong answers,' 40% of their time was spent chewing on a pencil."

So the questions that I want to ask are basically what would be assessed with a repeated measures ANOVA:
1) Does the percentages of time spent engaging in any one behavior differ from the percentages of time engaging in any of the other behaviors? (i.e., is there a main effect of behavior)

2) Do the percentages of time spent in any single behavior differ between the right-answer and wrong-answer groups? (i.e., is there a main effect for 'group'?)

and

3) Is there an interaction?

So, why can't I just do a repeated measures ANOVA? Because all the values are interdependent proportions. For any participant to spend more time looking up, he will necessarily be spending less time looking down. (Yes, you could imagine that maybe if he looks up, that extra percentage comes from a different behavior, but we can't guarantee that).

How do I analyze this data to look for significant differences? Thanks!