i've hugeled all my garden beds and i can tell you, digging down 3 feet is more of a lofty goal and probably by the last bed a far cry from the reality. lol. 3 feet is great, your setup looks lovely.
As for order, I'd put the wood in first, then small branches, then some smaller stuff, add some slop from your buckets, then whatever organic matter you have hanging around (
hay, leaves, shredded stuff) and then the dirt on top. i didn't catch if you're adding external dirt or going to use what you have in there (in which case you'll need to dig it out while you put all that good stuff in the beds).
Whether you'll have critters invading basically depends on what kind of critters you have, and luck. if you have rat issues, maybe i'd consider putting the slop on top of the largest wood and under the smaller stuff (not so close to the surface, in other words), although honestly I trench compost a lot and almost never have problems. (again, your varmints may vary)
I also wouldn't worry about the mycorrhizae and microorganisms. They will all show up once it starts warming up.
You've got some good suggestions already. Urine is good, biochar is good, nature is good at rotting stuff down, I think you're going to have a great garden.