So it's not as bad as we thought it was. Jeff called. It turns out that back in 2004, when we gave Duke and Daisy away, I asked their new owner to contact us first if she ever needed to find them a new home. It turns out that although I forgot that promise, she didn't. Hence the phonecall.
In addition, her time with our pooches solidly confirmed in her mind their need to always be together. And so she's committed to finding them a home together. No pound for Duke and Daisy. Luckily, she has some good contacts to help her in the search for a new home, including a Lab breeder and a Greyhound rescue, so we're all pretty sure they'll find a good new patch of grass together.
I'm much relieved. Now we can all rest easy.