What bit did they use to cut the slots on the waste board to screw to the carriage? Looks like they may have used 2 different ones?
You can use a slot / key hole bit.
Here is another take, using a single straight bit like 1/4":
- Get some 1/2" MDF, prepare two full boards.
- Mount the first one, carve slots that are say 1/2" wide (wide and deep enough to accept your square nut)
- Screw / glue the second board up, on top of the first one.
- Now carve a 1/4" slot, center aligned with the 1/2" slot, all the way through the top board.
Presto 
Good advice thanks
How well does mdf hold the bolts? I made my clamps out of 1/2" mdf and even with washers (which wouldn’t fit in the slots) they get chewed up pretty quickly.