Turns out it's a good idea when freezing a frame to set the velocity by right-clicking the velocity envelope keyframe and typing in "0". I had the odd experience of freezing a bunch clips for a 30 second duration by pulling the velocity envelope down with the mouse.
Even though "0%" was displayed, the actual speed was something like "0.02%". After rendering I could see my image creeping almost imperceptibly along, and rendering took MUCH longer than after I realized what was going on and set the velocity to real zero.