Thanks all for your feedback!

As to the actual powers, one other thing that might be worth thinking about:

"All ogres have an innate capacity for neutralizing magical forces to one degree or another. "  (Summer Knight, ch. 12).

Thanks a lot, I wasn't considering this before.

A stacked catch with magic immunity.

That however seems a bit much, especially since physical immunity seems to be reserved for NPCs. Not sure if there is a smaller version? Some kind of resistance, but not immunity, to magic?

If the change is purely physical, you don’t need beast shape because you wouldn’t need to swap skills.  And there’s less balance issues if you can’t swap your skills.

Yeah, that is interesting. However it strikes me as weird that the Hulk form would have the same set of skills as the human form.

Yes, that's what I was saying. 

- since your setting idea is very broad you could try the world creation together with your players. Fate Core has a good guide on this.
- If you want to play Fate in your own Setting, then DFRPG is a bad game to start with. There are a lot better Fate systems you can use and are available for free. DFRPG moved quite a bit away from the core spirit of Fate
-for high Fantasy I can recommend checking out the Atomic Robo ruleset. It sounds a bit far fetched but it would actually be quite a good fit for high fantasy as well. It's also an improved (imho) version of the fate core rules
- use the fate systems toolkit to decide how magic should work in your world. That's probably going to be the most important decision you have to make upfront.

How customize-able are the characters?

One thing that's always put me off FAE is that the characters feel same-y to me, I'm hoping the Dresden Files variant manages to avoid that.

you still have the high concept, trouble and three additional aspects so there's enough space for customization. The numbers on your sheet don't really matter much anyway.

same

But...Well, it seems that players need to be reactive when they should be proactive and vice versa. For instance, suppose I'm taking cover behind a concrete slab, beyond which are 5 goons with AK-47s trying to gun me down. If the GM is playing it correctly, and I'm understanding the system correctly, I can only "tag" the cover against one of those goons.

Well, in Fate, you're the star in an action flick. Nobody wants to see you hide behind a concrete slab for fifteen minutes of the movie. You hide for a short cut, then jump out and drive the story forward. Fate - the system - rewards you accordingly.

Also, in that scene, the 5 goons should count as one mob with one attack, assuming they're faceless.

Thanks a lot for all these great suggestions! Especially for all the aspect ideas, Shaft.
I am more or less settled on choosing Bear instead of Coyote. Also, I am sticking with the Emissary of Power Template, and chose "Last Emissary of the Bear" as my High Concept: With the recent disturbances of power, Bear decided one last time to grant his dwindling power to somebody from the tribe.
Also Beast Change is great, it allows me to skill both shapes separately, so I am most likely going to go with that.