The timing on the Climax is very sensible. By rotating the joint 45 degrees, you effectively have moved the oscillation waveform half a cycle over. This effetively reverses the effects of joint geometry on oscillations.
With two joints separated by 45 degress, joints bent in the same dirction within a plane SUBTRACT and joints bent in opposite directions ADD. This is the reverse of aligned joints. So, when corning, 45 offset joints compensate perfectly when at the same angle. (Boy those guys ere clever)
I would bet Heislers ae set up the same way. It would also make sense for Shays IF the engine set (and the rest of the line shaft for that matter) were set up in a perfect line. An offset in the line shaft with 45 offset joints would be very bad, effctively doubling the oscillations of the center shaft to the ouput shaft.
Are we sure that Shay joints are algned and not 45 degress separated? I assumed they were aligned, but if they are not, that changes everything around.