I've tried lots of different approaches to standing up as the quad has evolved.  The most recent variant used a low-torque non-IK sweep to get the legs into a position, where IK could be used to stand up.  However, since the legs did their initial prepositioning with no IK, the legs would usually drag across the ground.  On some surfaces with a lot of friction, they could get stuck and never reach the target position.

So, I updated it yet again, to add another phase.  Now, the shoulders lift the legs well clear of the ground, then the lower two joints sweep into position, and then the IK sequence is used to stand up.  The result is that now it can easily stand up even on EVA foam: