So Tilly's figured out that she has to sit to cross the road, so she sits when she wants to cross the road to go a different way. Today, we ended up walking on the other side of the road, so we walked to the point where she was lost - her tail went down, and she was starting to look worried. I suggested we go a different way to get back to a road she knew, and she perked right up.
I found an OS/X install image for a bootable USB flash drive, so I downloaded that, copied it to my flash drive and re-installed Jen's Mac, and this time restoring from the Time Machine backup worked just fine. Yay! Of course, she doesn't need to pick it up until next week, but whatever.