With that structure in mind, after Anakin "stays the course" as you put it, he should be a committed, cool headed Jedi. His rushing in to face Dooku fits with his early character as an overconfident rebel, but over the course of the film he's matured. So the question becomes how to rectify the situation? In TM's original plans he was just going to cut away from the duel as soon the the three confronted each other, then cut back to reveal Anakin had been made quick work of. This would be very choppy however, and just wouldn't feel right. Add to that the RotS line, "This time we'll take him together." The idea was to remove force lightning from the duel, which is essential as well. But how can Anakin be taken out of the duel? A force push? The fact of the matter is it is a poorly conceived confrontation, and Dooku was made far too powerful for the sole purpose of giving Yoda someone to fight (which should have, and will be in this edit, been saved for Episode III). I honestly have no good ideas on solving this, but I’m sure someone in our esteemed think tank will be able to come up with something.
It’s interesting to note that major problems with TPM and AotC are the lack of a story arc for Anakin. We’ve discussed this before, but his character is all over the place in both films. He seems to have gradual, though sometimes sporadic, character growth through the course of the films, but at their climax he reverts back to who he was at the beginning. Luke maintained his development and matured over the course of the OT, as he was obviously not the same person he was at the beginning of ANH or ESB when those films had concluded.