Thanks, jikkme, for the great illustrated walk-through! Took a while, but I got my light pipe out.
Actually fixing the thing turned out to be the hardest part -- the mirrors are really small and delicate to work with. I used Krazy Glue to rebuild the collapsed side and reinforce the other side, but a little bit of the glue leaked into the inside of the pipe and now causes a visible shadow in the upper-right corner of the screen. The situation is much much better than it was before, but now I wish I'd used an epoxy.
I'm sure I'll have to go back in again one day, though -- the construction of the light pipe is terrible! Glass glued to glass and then the join put under a shear load by the clip that holds it in place. No wonder this is such a common problem.
As for the color wheel, I used some 18 gauge wire to tie its mounting assembly to the nearby heat sink, up and out of the way, while working on the light tunnel. There really isn't anywhere to set it down in a stable way with the short reach of the ribbon cable.