Well I opened up the differential and answered my own question. It looks like I had a bunch of gunk covering the output shaft, but no leak. And my learning for this part is - if the drivers side is not leaking, don't fix it!
To get the driver's side output shaft out remove the three bolts securing the triangular cover behind the drivers side shaft. Once you remove the bolts, the cover and shaft slide out of the diff as an assembly.
Now - note there are two seals. There is a simple seal like a squared off o-ring about 3 inches in diameter that seals off the triangular cover. If you had a leak from the edge of the cover, this would be the seal to replace. In my case the seal stuck to the differential housing. If this happens to you, remove it, clean it, and then reinstall it in the groove on the back of the triangular cover.
There is also a shaft seal - this is what I had assumed I should be replacing since it's counterpart of the passenger side had been leaking badly. This would be the seal to replace if you saw a leak coming from around the output shaft. Unfortunately, the drivers side shaft seal is hidden behind a what appears to be press-fit bearing. I removed the snap ring retaining the bearing, and the bearing was still stuck on tight. So I am going to leave the whole thing alone.
The net is that it looks to me like if you do get a leak coming from the drivers side output shaft, you will need a new bearing as well as a new seal, and you'll need to press off the old bearing, replace the seal and then press on a new bearing. If you get a leak coming from the edges of the cover on the drivers side, you are in luck and you just have a simple o-ring like seal to replace.
I thoroughly cleaned and re-oiled the bearing before reassembly
The passenger side is much easier. Remove the single bolt in the center of the output shaft. Pull the output shaft out. The seal is right in front of you, and it's easy to remove and replace.
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