Once I set the "Pin Number" property on one of my terminal pads in the module version of this board (https://www.flux.ai/whitelynx/mx-single-keyswitch-hot-swap-board-module?editor=pcb_3d), the custom copper pad logo moves to be attached to the board surface in the 3D view, though it is still way too thick.

It seems like the copper pad is just rendered way too far down; if I have a big enough layout and zoom out in the 3D view looking at the bottom of the board, it shows up, but is cropped to the layout border.