.... As you identified at the end, the correct solution for this problem is a job queue. There is nothing about PHP that prevents the use of a job queue - in fact the shared-nothing, process-per-request model almost encourages the developer to offload as much work as possible to a job queue..

Using Wordpress (or it's plugins) as any kind of reference for what PHP is capable of, is like using McDonalds as the basis for a cook book.