How to remove a screen that is shattered into hundreds of tiny pieces

From my understanding of your issue, you probably need something to act as a brace that will rigidly hold the shards in place, since the tape is too flexible.

You could perhaps glue a popsicle stick or a ruler to the glass near the edge so that it all lifts up uniformly due to the rigidity of the wood, but I have never tried this before. Since the glass is already absolutely obliterated, you don't have much to lose, but I would still be careful with how you apply glue to avoid damaging the logic board beneath.

Could you perhaps provide some images?