Curt,
One of those pictures looks awfully familiar!
I think everyone's got you on the right track, using a seal puller or something to
carefully pry out the remainder of the old seal. The thing is to get it moving out straight. Any tool you can get under it will probably work, but you'll have to work your way around a tiny bit at a time. A little heat, not too much, should soften up the old rubber and might help too. If it's brittle it's going to be tough not to lose a few fragments down into the differential, but that's the case either way.
One thing that bears looking at closer is what looks to be a small notch in your outer sealing surface, into which the old seal projects. (Circled below) Is that what I'm seeing? Mine definitely didn't have anything like that, and the new seal won't seal if that's the case.
I'm not experienced to know if that was standard for some cases, but hopefully some others here can offer more insight.
Mike