Installation:
Dragged all the knocked down parts to the basement. I screwed the shelf back together in the hallway, then fit my little platform in the utility room where it is going to live.
Then I dropped the shelf in place between the studs, and secured it to the platform with pocket-screws from the underside of the base. It also has two screws driven through the studs towards the top to keep it from tipping.
Fit like a glove. Well, a semi-tight glove, just in case the walls settle or shift. A little glue and the application of the face-frame finished the job.
This seems so much nicer and less likely to catch fire than the previous jumble we had. I am very content with it. And thus ends my first completed project for 2020!