I thought I'd come back and post pictures, as promised. It's been several months of working when I got the chance - mostly on the weekends. Many lessons learned, and a truckload of triangles later (lots of diagonal cuts!), here is the payoff.
I'm pretty happy with the results, but there are some gaps and things got pretty loose as I ran out of space to use the floor nailer. I'm not sure I would do the compound cuts again to butt against the railing base - it made precision measurements to meet thresholds difficult. The cat is still with us but confined to a bedroom when we're not at home.
Thanks for all the advice when I started the project!