Maybe I'm being a little dense here, but why couldn't you attach a couple of floats to the thing and just cut it loose when seas permitted? Then you can circle about and pick it up alongside with little way on.
Given the general idea is free and the fact that one can make them with six hours of effort on a sewing machine, is it ridiculous to consider them disposable post-storm? I wouldn't want to dump a para-anchor-type sea anchor (too expensive) but a Jordan series drogue is simply a hundred cloth cones on the sort of line you can easily replace.
Or am I missing something?