Should I use the Transients API to temporarily hold edited attachements?

Transients would be a good option for sure assuming the data is crop instructions only. Transients work best performance-wise if you have memcached installed as well as an object cache plugin. As a caveat, don’t rely on object cache to be 100% solid. It is volatile and can be corrupted rather easily. I’ve found this to be quite true at times.

If you want a more fail-safe storage, you could just use transients without object cache as the key/value pairs will be stored as an expiring option in the options table.

Either way, transients are a convenient way to store temporary data. I would check out Mark Jaquith’s TLC Transient class. It’s a huge help getting transients setup in your theme.