Long outputs will tend to naturally deteriorate, as it tries to reproduce the existing deterioration and accidentally adds some more. Better: Sample one tag at a time. Shuffle the inputs every time to access different subdistributions. (I wonder how much the subdistributions differ for two random shuffles...) If you output the tag that has the highest minimum probability in each of a hundred subdistributions, I bet that’ll produce a tag that’s not in the inputs.
Long outputs will tend to naturally deteriorate, as it tries to reproduce the existing deterioration and accidentally adds some more. Better: Sample one tag at a time. Shuffle the inputs every time to access different subdistributions. (I wonder how much the subdistributions differ for two random shuffles...) If you output the tag that has the highest minimum probability in each of a hundred subdistributions, I bet that’ll produce a tag that’s not in the inputs.
Shuffling would also be good to combat the alphabetic order, which has got to be skewing output somehow.