Prusament Neon Green Transparent PETG - for the Tower
Prusament Azure Blue PLA - for the trays and pins. (you'll want to print these in a more malleable filament to make plugging in the pins easier.)
Used default parameters in Slic3r with the Original Prusa i3 MK3S.
Thanks for the suggestions for using a heat gun or warm water to prime the pins sliding into the holes. Be careful not to overdo the heat, but if you do, just reprint the pins and try again.
Love this thing, and we're going to get some heavy use tonight for board games!
Neon Green Transparent PETG, Azure Blue PLA