...
Now, the extra commitment in the UTXO makes computing the hashes more expensive. Instead of a single hash, you need to compute 12-13 Hashes for the Merkle root (if you still use Merkle grinding to generate the commitment hashes). But it requires no extra storage. So the total extra cost is 12-13 GHash/s for a 400 PHash/s pool. Everything else is unchanged.
With segwit active, a single transaction with 13 inputs and 13 outputs all signed ANYONECANPAY|SINGLE, it's possible to permute the pairs to get 13! permutations without the need to re-sign, as ANYONECANPAY|SINGLE in segwit outpoints does not commit to the specific place of the pair.
If the 13 inputs are derived from the same transaction, and the outputs are all the same, you should really only need to swap 13 bytes around the serialized transaction to generate a different, valid transaction and txid. not true, might be true if the inputs are not signed at all.