Honestly, it's much less hassle to just enable BitLocker on the drive, and then employ a highly decorated secure offsite backup solution. BitLocker is pretty-much guaranteed not to corrupt any of your files, or interfere with any of your work. All of us employees at Microsoft are required to have BitLocker enabled on our workstations at all times, and it's never caused anyone an ounce of grief that I know of.
I'm not totally sure what types of offsite backup services will meet your security needs, but if you can find a service that is FISMA and HIPAA certified, you should be good to go. These services usually have decent user interfaces, that are geared toward minimal interference with your regular operations.