I'm hoping we've made a breakthrough with Charles. It has come in the form of an index card.
I read some posts and comments on the forums of The Homeschool Lounge, which is a website that is so encouraging for homeschool moms. I took some of what I read there as confirmation that these struggles may be in part due to the stage of life he is entering. I decided to back off a little.
I wrote all his assignments on a big index card and gathered his books and papers, showing him exactly where everything was. (It was all gathered, he just never really noticed that his things were organized and placed in the same spot. Now he knows.) I made sure he knew exactly what would happen if he did not complete his work. (The big motivator now is time on the computer. The rule is no screens until school work is complete) I tried to explain the details I knew he'd ask about and then I did not nag him to get work done. I told him that school was done at 4 and that any work not completed by then would have to be done the next day
The first day he wasted time until about 4 pm, only intermittently working and allowing himself to get distracted many, many times. Then I told him he could stop working and put his school things away, but I gave him a choice to finish so he could have screen privileges. He worked longer and completed what he'd been dragging his feet to finish for the past three hours in less than one.
Today Gaylen lectured them about wasting time while I was gone to the library and after that both were more focussed. Charles keeps talking about how the card helps him and I have seen the beginnings of self-motivation.
Time will tell and I'm sure we'll have so many more times when they all push the boundaries, but there may just be a light at the end of the tunnel. I'll be in prayer for more inspiration for those trying times!