To try to get rid of duplicate designs could you classify each puzzle with how many of each type of piece it has, then go through to check if two puzzles with the same pieces are copies or not?
The filtering program already did that.
If anybody is interested. I wrote an article for CFF about the filtering used for this list this program. It was published in CFF #79 but still left out many details.
To make a long story short:
Of all variants that can be transformed into each other by (1) twisting the layers and/or (2) twisting the whole puzzle and/or (3) mirroring the whole puzzle at most one is present in the resulting list.
If the variant has one or more implicit bonds the variant is deleted since there will be a variant on the list where this bond is explicit. A bond is implicit when it is not set but leaving it unset does not allow new moves.
If a unset bond does not change anything but open one or more dead ends the variant is omitted. This inspiration for this rule was given to my by Bram 7 years ago in the thread Carl linked to. Thank you Bram for that.
There are two more filtering criterias I found but have not generalized to other puzzles yet. There might be more ideas but I haven't had them so far.
You are still missing my favorite bandaged 3x3x3(I think), a fused cornerblock and a fused edge group.
Please explain what a cornerblock and a fused edge group is.
Do they have size 1x2x3 or 1x1x3 or anything else?
Edit: Corrected a quote.