I’m happy to report success. Using a single clearance hole through both the rear face and the small side pieces I was able to get everything into place with no splitting. I used thin one inch screws to put the front liner on using pilot holes before screwing it in place. To position everything it really helped to double stick all 4 pieces together. Despite (or perhaps because of) the difficulty I had, I feel quite good about getting this done and I’m happy with the results.