Slightly over-engineered. Better built. Slightly less tip angle this time.
Two right-angle triangles joined by a couple of 2.5" pieces of 1x1 create the tip angle for the demi support bed. One of those pieces of 1x1 is screwed to the baseboard, the other to the demi support bed. So it's all fully rigid.
Two more (identical) triangles used as demi side supports, screwed to 1x1x1 blocks which are screwed to the support bed. Their factory-cut edges are used against the demi, but a bit of cushioning foam stuff has been glued there as well, demi sides ain't as straight as you might excpect. Angled in so the touching faces are normal to the demi's sides - should cope well with varying diameters (crosses fingers)
I just want to glue something non-slip to the bottom of the baseboard and the top of the support bed (partly to cover the screwheads) and I'm done, but I don't seem to have anything suitable. Oh and I might inject glue into all the joints, just for the fun of getting the glue-gun out.