I can tell you what I did to get mine to work.. I placed a thin sheet of metal flashing beneath my die and ran it through the big shot machine,cut side up and between the two plastic plates. You still may have to roll the die cut around a marker to get the tiny pieces to pop out but now they come out.
If you feel resistance when rolling it thru the machine stop... if you break your big shot machine, it won't be covered by the warranty as flashing hasn't been tested by su or sizzix or provocraft, etc... my machine is very loose, so I had to use a piece of flashing with a shim... I made a permanent shim by cutting a piece of sticky sheet the same size as the flashing and removing only one of the paper covers from the sheet (leave the other en tact). The flashing can be sharp along the edges, so I used a 1/4" corner rounder to round the edges and make it safer. I think the reason it works is because both plastic plates and the doily die are flexed when pushed through the machine... the flashing is more solid??