Unclear on double-hashing previous Transaction when creating a new Transaction
I've figured it out.

So in this case (and if you look up a previous transaction on sites like blockchain.info) the transaction ID is already the double-hashed transaction. The input to the new transaction is just the reverse of the transaction ID.

So my previous transaction starts:
90 72 c9 13 ...

and the full transaction created by coinb.in ends in:
... 13 c9 72 90