I highly recommend using SuperDuper! to do what you need. I've used it for years now and have had 0 problems with it. It's fast, powerful, and offers a lot of flexibility.
Thanks to all for the helpful feedback.
I downloaded a trial version of SuperDuper and read the User's Guide and agree that it does what I need - and more. And very clearly documented. Many functions become active only after purchase. Costs only $28.
One benefit of this solution is that I can continue to use Time Machine to back up my internal startup drive to a dedicated external drive, while also using SuperDuper to back up my RAW pic files on their own external drive to an another external backup drive. SuperDuper allows for flexible backup scheduling.
Cautions about LaCie hard drive reliability are also appreciated!