You could use the DOE platform to create the gage study table and then use a Col Shuffle formula to randomize the parts within the parts column.
When creating the DOE matrix (i.e. the gage study table) represent each part by a number (1,2,3,...) then do the following:
1) Add a formula to the part column (right click on column header --> select Formula).
2) Once the formula menu is opened, in the function list select "Random", a list will open
3) From the list select "Col Shuffle" (down towards bottom of list)
4) Click on the Apply button and you will see your part column randomize before your very eyes.
Creating a formula: http://www.jmp.com/support/help/Create_a_Formula.shtml
Col Shuffle: http://www.jmp.com/support/help/Random_Functions_2.shtml