Well guys, I don't really know any more. I do know he made me give a 61.31d endorsement and since I was there I just wrote one real quick. And perhaps I (and he?) didn't read down the list far enough, I don't know. So I started endorsing everybody for 61.31d, even for different DPEs. As I never heard anything back (of course, you wouldn't necessarily hear about an over-endorsement), I just kept doing it because it "must" be the right thing.
The solo endorsement for Private likely doesn't come up very often, because most checkrides likely take place within 90 days of the last solo endorsement, so whether or not it's needed, it's already there.