Sorry bud. Turns out the math for blending rotated surfaces is ridiculously hard.
If you're desperate, you could try taking your rotated slices and send them 1:1 into a virtual screen each, making each virtual the size of the rotated bounds of its input, blend those virtuals, and then in the actual output screens, slice out the rotated shape from the virtuals and rotate that upright to send to the projector. The physical rotation will put the image straight again, and it should have the blend in the correct corners. Theoretically.
If that is making your head spin, it's exactly what we'd need to calculate for you in offscreen render targets in order to have rotated blends. And it's making our head spin too.