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Do the center back braces get installed as one piece and the crossbracing notched to fit or are the cross braces installed and the center brace applied as pieces between cross braces?

You can do it either way, whatever works best for you. The final result comes out the same. I've done it both ways, and I prefer gluing down the strip, then notching for the braces. I know the strip is straight this way. If you piece between the braces, a little harder to line up straight, but not that difficult, and in reality, who would see or notice if they were off a 1/32" or so through the sound hole, right?

I do the cross grain first
that way I know it is straight , I can also sand a nice shape to it and burnish it to make it look finished.
Then I cut the channel to set in the braces.

I had tried gluing the in separate and never had good luck in making them appear finished.

the back cross grain should be flexible along the seam. Also you don't really want a support here with the same grain direction of the back. That is why spruce works so well here. It is strong yet flexible.

I glue the center seam reinforcement strip in, then notch it for the braces. Personal preference.

I have done both thinking that cutting the notches afterward would be more difficult - it is MUCH easier. Mark the ends of your braces on the back, glue the center strip full length, set the braces on the center strip with the ends in the right places, use a sharp chisel with the bevel out to just barely mark the top of the back strip, saw inside that line, then pare across the back to the line - easy peasy

Ed