>>Got it. We need to have a symplesiomorphy in our paraphyletic group that is not present in the excluded taxa. Fine.
>>
>>I hereby create the "Nonchelonia". This taxon includes all organisms that posess a sacrum not covered by a carapace of fused ribs.>>

Taxonomy is a democracy. Anyone can propose any taxon for any reason, including of course the hatred of paraphyletic taxa among cladists. What you need is to publish your taxonomic proposal. Good luck.