Not OP, but I also use flat keycaps, so I thought I'd chime in. I'm not really sure why your hands would hurt with flat keycaps, but one of the reasons I chose to use flats were to allow for easier chording with Plover.
I don't know how to answer you exactly. My hands don't hurt. Maybe it's because of the combo of the ortholinear keyboard and the Dvorak layout causing me to move my fingers minimally.