So the problem has only gotten stranger. It's not the pads. Maybe I'm just not so good at bleeding my lines?...
I took off the brake pads, leaving the calipers hooked up to the hydraulic lines, and pulled on the brake lever. Both pistons showed the same jagged movement as before. So I squeezed them out, inspected them, pushed them back in (and they went in smooth), bled the whole system, and viola, the brakes were smooth as silk.... for about 5 minutes. The jagged movement slowly crept back in. Bled them again, ran fine again, and the same thing happened.
Is air leaking into the system? Is something else going on I'm not thinking about?