Hi Kevin,
If you 'move' an invoice (ie copy an invoice but to the same batch, rather than a different batch), then that invoice gets put at the bottom. This could be useful for existing invoices in a batch.
If you highlight an invoice and press the 'insert' key on your keyboard, that will create a new invoice above the highlighted record. This would be useful for adding new invoices in a batch.
And in the next release of Adagio Invoices, you will be able to sort invoices within a batch. Though 'short name' is not a field stored in Adagio Invoices batches, so it isn't available to sort by. Customer name will be available.