But I still don't fully understand. Is the basic idea to bring my chest up and create tension throughout my body?
I think that description works, yes. Let's take it too far in either direction to describe "un-wedged" and it may make more sense. If you're leaned over too far over the bar (think stiff-leg deadlift, or bar is just too far forward of your body), you won't be getting leverage under it, and you won't feel wedged and you'd have to do much of the lift with your back. Conversely, if you're squatted down too much to "lift with the legs" and/or leaning back trying to pull the bar backwards, you also won't be wedged under the weight. The "equally loaded between your feet and hands" is useful to a degree, but I'm not sure it would clue you into these position errors. Personally I think wedging is more of spreading the load to all the muscles in your legs, hips, and back. You feel them all loaded, then you initiate movement to get the weight up. Cues for doing that will vary with the method.
Wedging is accomplishing basically what the SS Step 4 is doing, but coming at it a totally different way. Both ways can work. Overall for deadlifting I'm partial to the SS method myself, but as @Steve Freides rightly pointed out, this forum isn't here for teaching another method. In my defense, one of the reasons I love the SS method is there are so many great resources out there to support it, such as the video @Alan Mackey provided above. While I truly appreciate articles and videos such as the one linked in this thread by @Brett Jones, they are few and far between, and I feel there's still a lot of room for improvement in StrongFirst's teaching this critically important lift. But this is only my opinion... offered with a genuine love and appreciation of StrongFirst.
Also, do you feel I'm bringing the bar down too slowly?
Personally I would bring it down a little faster, but I don't see a problem with how you're doing it.