So. I finished the strips last night and did a wet block overnight. I had two different skeins (top and bottom) and then for the middle skein knit two rows from one skein and two from the next. Blocked them out so they're about thirty inches long each. So far so good.
Today I braided them. The first time the top got all wonky--I couldn't figure out how to lay it out flat. Then I stuck a stitch holder in there and then it all started to make sense. I realized at this point that my strips were too wide and that the braid wasn't really going to look like a braid. But anyway, from here I knit about an inch of garter stitch and then I grafted both eds together. I also sewed some of the pieces together in the back so that it wouldn't undo itself and would lay well.
I still have some grafting to do but, yeah, the whole 'braided thing' kind of got lost. It still looks kind of cool and I'm sure I'll wear it (once I weave in the ends), but just not as cool as I hoped.
So live and learn. Next time, knit an inch of garter before starting the strips (I only did a couple of rows), do thinner strips, and maybe get a bit more length.