Whenever I load a mocap video from Recorder to Studio, my motion capped figure is always halfway beneath the floor plane. Ground-height fine-tuning isn't enough to fix it, and even if I place the rig perfectly on my mocap figure, "Refit pose" always throws the rig over the floor plane. Also, the floor always gets tilted by a few degrees for no reason (my Kinect is not tilted IRL).

The ground plane is detected automatically if there is sufficient floor area visible to a Kinect. Ensure that the floor of capture area is clean from unnecessary items and well visible to Kinect, and there are not much yellow pixels (noise) on the depth image of the floor. You may share one of your videos so I can make more specific recommendations.

So I should fit more floor in the shot?

It's hard to say not seeing an actual video. A rule of thumb is that the floor points should occupy at least 1/6 of the frame area.
BTW do you get any warning when evaluating background in iPi Recorder? It does some checks about the floor automatically.

No warnings with evaluation. Thanks for the 1/6 rule, though, I'll adjust my framing accordingly.