Solution: a wall-mounted toilet.
This is a special Geberit model that mounts directly into the wall. It doesn't touch the floor at all. The porcelain bowl will be supported by the hefty blue steel frame you see here, which is, in turn, bolted to a pair of 2x6 studs on either side. The water tank and everything fit between the studs, so there's no visible tank, no hardware, no nothing. The flush "handle" is really two pushbuttons that will mount on the wall above the bowl. Because it's a water-saving model, it even has two buttons, with one using half as much water as the other. (I'm thinking of labeling them #1 and #2.)
The real point of all this is that the wall-mounted drain will exit above the floor, instead of down through the floor like a conventional toilet. That allows us to plumb it up to our funky raised drain pipe without doing anything weird like building a platform or hiding the pipe inside a raised box. Very neat and tidy. This arrangement has the added benefit of moving the toilet slightly further into the room and away from the sloped ceiling, which means less chance of hitting your head. I love it when a plan comes together.