And unless I'm missing something, doesn't injecting PHP either require a plug-in or actively building on to a wordpress component?
Most implementations are massively bloated as a legacy from the jQuery days when that was neccessary. CSS is incredibly powerful now, and the browsers are all evergreen, so it's pretty trivial to implement a pure CSS/HTML gallery:
https://css-tricks.com/css-only-carousel/
This is fully featured, with indexing, scrolling, animation, etc., but you could slim that down even further to just a few lines for a simple automated slider. Obviously doesn't work if you need managed control, but 99% of gallery use-cases are just flipping through a homepage hero like the OP.
Regardless, my motivation was to implement as little as possible, as the whole motivation to switch to Wordpress was to not minimize what I'd have to build. I will make a note to detail that better in the future. Appreciate the candor.