As of COB Friday, I had ended up Dockerizing it. The default official PHP 7 pull took care of most of what I needed, just having to add Postgres to the Dockerfile -- which required an apt-get to load the postgres-devel stuff, much the same as you suggested above for compiling it manually. Looks like it worked -- at least where it failed was after the point where it would have read from the DB, and the failure had nothing to do with the PHP config. 🙂
Anyway, just wanted to thank you again for the help, and I'm going to mark this resolved, even if it was more like "worked-around".
And in about 5 hours, I start my trek that will end up in the Dominican Republic for a week of sun, relaxation, and no programming. 🙂