Update:

I have gotten the Dawn Shard but I haven't gone into the raining Giza Plains yet. All these sidequests became available and I'm just wrapping them up now.

I've managed to get the Espers Adrammelech and Zalera. Both took two tries, even with a level 38 party. Barheim Passage is very tough, even now, so I just ran when I came to the room full of Dead Bones and Specters (although Pheonix Downs can take out the second guys). The last Esper I'm going to try to get is Cuchulainn, although he may be too tough.

I've done all the hunts that can be done in the areas I've already explored. Orthos gave me a lot of trouble, even with two rounds of Quickenings. Earth Tyrant was easier than I expected.

This is certainly one of the most sidequest-intensive FFs. Since I'm trying to do them all, the overleveling was worthwhile.