A few thoughts - my two older kids (now in college) told me that the challenge of thwarting my efforts to keep them up to date on homework was far more exciting and rewarding than doing work that they hated, was boring, and that they saw absolutely no need to do. Even when they were punished - taking away iPods, grounding them, etc., they said that learning they could "survive" the punishment was still more rewarding than doing work they hated.
Gifted kids - especially 2e - do not have the same currency as conventional wisdom might suggest, so not having a teacher yell at them, not missing out on lunch with friends, not getting punished at home - we would think these motivators would drive them to suffer through the work. Not so. My daughter recently confessed that she only read one book in four years of AP English in high school because it was more fun to see how much she could synthesize through classroom discussions. She got C's and saved herself hours of miserable reading - a very fair payoff in her mind.
Last thought - could it be a memory thing? My youngest has dyslexia and dysgraphia, and he can't remember a single instruction from the time it is uttered at the bottom of the stairs until he gets to the top. It is gone, forgotten.
Have you thought about negotiating which projects can take the hit of a zero and which should be done in exchange? It might save the crazy-making of avoiding ALL of them.
